College algebra 2nd edition julie miller pdf download

College algebra 2nd edition julie miller pdf download

College Algebra (Collegiate Math) 2nd Edition,Search Ebook here:

Click Done and download the resulting document. Our solution allows you to take the whole process of executing legal forms online. As a result, you save hours (if not days or weeks) and View PDF Textbooks: College Algebra, by Julie Miller, 2nd edition. Technology: A TI 83+, or an equivalent graphing calculator, is required. View PDF 2. Register with your SFA email and College Algebra 2nd Edition is written by Julie Miller and published by McGraw-Hill Higher Education. The Digital and eTextbook ISBNs for College Algebra are , Oct 15,  · Julie Miller Daytona State College Digital contributions from Donna Gerken Miami-Dade College Kendall COLLEGE ALGEBRA, SECOND EDITION Published by McGraw-Hill PDF File: College Algebra Julie Miller - PDF-CAJM 2/4 College Algebra Julie Miller This type of College Algebra Julie Miller can be a very detailed document. View PDF Get free access to ... read more

document iframe. When Julie Miller began writing her successful developmental math series one of her primary goals was to bridge the gap between preparatory courses and college algebra. With the Miller College Algebra series Julie has carried forward her clear concise writing style; highly effective pedagogical features; and complete author-created technological package to students in this course area. Previous page. Sticky notes. On Kindle Scribe. McGraw-Hill Higher Education. Publication date. January 8, File size. See all details. Next page. Due to its large file size, this book may take longer to download. Kindle e-Readers Kindle 5th Generation Kindle Keyboard Kindle DX Kindle 2nd Generation Kindle 1st Generation Kindle Paperwhite Kindle Paperwhite 5th Generation Kindle Touch Kindle Voyage Kindle Kindle Oasis.

Fire Tablets Kindle Fire HDX 8. Fire Phones Fire Phone. Free Kindle Reading Apps Kindle for Windows 8 Kindle for Windows Phone Kindle for BlackBerry Kindle for Android Phones Kindle for Android Tablets Kindle for iPhone Kindle for iPod Touch Kindle for iPad Kindle for Mac Kindle for PC Kindle Cloud Reader. Customers who viewed this item also viewed. Page 1 of 1 Start over Page 1 of 1. College Algebra. James Stewart. Kindle Edition. College Algebra DeMYSTiFieD, 2nd Edition. Rhonda Huettenmueller. Jay Abramson. Julie Miller. Mastering Algebra - Advanced Level: Over 2, Solved Problems Hamilton Education Guides Book 4. Dan Hamilton. Robert F. About the Author Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida.

In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers. My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. Brief content visible, double tap to read full content. Full content visible, double tap to read brief content. Help others learn more about this product by uploading a video!

About the author Follow authors to get new release updates, plus improved recommendations. Discover more of the author’s books, see similar authors, read author blogs and more. Read more Read less. Customer reviews. How customer reviews and ratings work Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them. Learn more how customers reviews work on Amazon. Images in this review. Reviews with images. See all customer images.

Top reviews Most recent Top reviews. Top reviews from the United States. There was a problem filtering reviews right now. Please try again later. Verified Purchase. It’s a good quality math book. It’s held up all semester and makes it easy to follow along with my class. Product was in good condition no rips and tears, came fairly quickly, did not come with access code because I rented the book, and there was no writing on it. Easy to use and navigate through online. This was a book my son needed for a college course. The exact distance is 4 units. This is approximately However, in the case of the Pythagorean theorem, the converse is a true statement. Answer 1. The Pythagorean theorem tells us that if a right triangle has legs of lengths a and b and hypotenuse of length c, then a2 1 b2 5 c2.

The following related statement is also true: If a2 1 b2 5 c2, then a triangle with sides of lengths a, b, and c is a right triangle. We use this important concept in Example 2. Solution: TIP We denote the distance between points P and Q as d P, Q or PQ. The second notation is the length of the line segment with endpoints P and Q. y Determine the distance between each pair of points. Label the shorter sides as a and b. Check the condition that a2 1 b2 5 c2. y x2, y2 x1 1 x2 , y1 1 y2 2 2 x1, y1 Now suppose that we want to find the midpoint of the line segment between the distinct points x1, y1 and x2, y2. The midpoint of a line segment is the point equidistant the same distance from the endpoints Figure The x-coordinate of the midpoint is the average of the x-coordinates from the endpoints.

Likewise, the y-coordinate of the midpoint is the average of the y-coordinates from the endpoints. x Figure Midpoint Formula The midpoint of the line segment with endpoints x1, y1 and x2, y2 is M5a x1 1 x2 y1 1 y2 , b 2 2 average of x-coordinates EXAMPLE 3 Avoiding Mistakes average of y-coordinates The midpoint of a line segment is an ordered pair with two coordinates , not a single number. Finding the Midpoint of a Line Segment Find the midpoint of the line segment with endpoints 4. y Solution: Answer 2. Apply the midpoint formula. Graph Equations by Plotting Points The relationship between two variables can often be expressed as a graph or expressed algebraically as an equation. For example, suppose that two variables, x and y, are related such that y is 2 more than x.

An equation to represent this relationship is y 5 x 1 2. A solution to an equation in the variables x and y is an ordered pair x, y that when substituted into the equation makes the equation a true statement. For example, the following ordered pairs are solutions to the equation y 5 x 1 2. The graph of all solutions to an equation is called the graph of the equation. The graph of y 5 x 1 2 is shown in Figure One of the goals of this text is to identify families of equations and the characteristics of their graphs.

As we proceed through the text, we will develop tools to graph equations efficiently. For now, we present the point-plotting method to graph the solution set of an equation. In Example 4, we start by selecting several values of x and using the equation to calculate the corresponding values of y. Then we plot the points to form a general outline of the curve. EXAMPLE 4 Graphing an Equation by Plotting Points Graph the equation by plotting points. Then use the equation to calculate the corresponding y values. Therefore, the values of x must be chosen so that when substituted into the equation, they produce a real number for y. Sometimes the values of x must be restricted to produce real numbers for y. This is demonstrated in Example 5.

EXAMPLE 5 Graphing an Equation by Plotting Points Graph the equation by plotting points. Apply the square root property. y TIP x In Example 5, we choose several convenient values of x such as 21, 0, 3, and 8 so that the radicand will be a perfect square. Identify x- and y-Intercepts y When analyzing graphs, we want to examine their most important features. Two key features are the x- and y-intercepts of a graph. These are the points where a graph intersects the x- and y-axes. Any point on the x-axis has a y-coordinate of zero. Therefore, an x-intercept is a point a, 0 where a graph intersects the x-axis Figure Any point on the y-axis has an x-coordinate of zero. Therefore, a y-intercept is a point 0, b where a graph intersects the y-axis Figure For example, if an x-intercept is 24, 0 , then the x-intercept may be stated simply as 24 the y-coordinate is understood to be zero.

Similarly, we may refer to a y-intercept as the y-coordinate of a point of intersection that a graph makes with the y-axis. For example, if a y-intercept is 0, 2 , then it may be stated simply as 2. Answer y 5. x1 y2 52 To find the x- and y-intercepts from an equation in x and y, follow these steps. Find the x-intercept s. Find the y-intercept s. y 0 0x0 x 5 5 5 5 0x0 2 1 0x0 2 1 1 1 or x 5 21 To find the x-intercept s , substitute 0 for y and solve for x. Isolate the absolute value. Recall that for k. The x-intercepts are 1, 0 and 21, 0. The y-intercept is 0, The intercepts 1, 0 , 21, 0 , and 0, 21 are consistent with the graph of the equation y 5 0 x 0 2 1 found in Example 4 Figure Skill Practice 6 Given the equation y 5 x2 2 4, a. TIP Sometimes when solving for an x- or y-intercept, we encounter an equation with an imaginary solution. In such a case, the graph has no x- or y-intercept. Graph Equations Using a Graphing Utility Answers 6. We will quickly enhance this method with other techniques that are less cumbersome and use more analysis and strategy.

One weakness of the point-plotting method is that it may be slow to execute by pencil and paper. Also, the selected points must fairly represent the shape of the graph. Otherwise the sketch will be inaccurate. Graphing utilities can help with both of these weaknesses. They can graph many points quickly, and the more points that are plotted, the greater the likelihood that we see the key features of the graph. Graphing utilities include graphing calculators, spreadsheets, specialty graphing programs, and apps on phones. Figures and show a table and a graph for y 5 x2 2 3. Notice that the calculator expects the equation represented with the y variable isolated. To set up a table, enter the starting value for x, in this case, Then set the increment by which to increase x, in this case 1. Figure The table shows eleven x-y pairs but more can be accessed by using the up and down arrow keys on the keypad. In this context, it represents the change from one value of x to the next.

The graph in Figure is shown between x and y values from to The tick marks on the axes are 1 unit apart. The viewing window with these parameters is denoted [, 10, 1] by [, 10, 1]. minimum x value TIP The calculator plots a large number of points and then connects the points. So instead of graphing a single smooth curve, it graphs a series of short line segments. This may give the graph a jagged look Figure maximum x value minimum y value maximum y value 10 [, 10, 1] by [, 10, 1]. Solution: Enter the equations using the Y5 editor. Use the WINDOW editor to change the viewing window parameters. The variables Xmin, Xmax, and Xscl relate to [, 20, 2]. The variables Ymin, Ymax, and Yscl relate to [, 15, 3]. Notice that the graphs of both equations appear.

This provides us with a tool for visually examining two different models at the same time. Simplify the radical. Solve for y. ax 1 by 5 c Evaluate x2 1 4x 1 5 for x 5 25 Concept Connections 1. In a rectangular coordinate system, the point where the x- and y-axes meet is called the 2. The x- and y-axes divide the coordinate plane into four regions called. The distance between two distinct points x1, y1 and x2, y2 is given by the formula. The midpoint of the line segment with endpoints x1, y1 and x2, y2 is given by the formula 5. to an equation in the variables x and y is an ordered pair x, y that makes the equation a true statement. An x-intercept of a graph has a y-coordinate of. A y-intercept of a graph has an x-coordinate of. Given an equation in the variables x and y, find the y-intercept by substituting for x and solving for Objective 1: Plot Points on a Rectangular Coordinate System For Exercises 9—10, plot the points on a rectangular coordinate system.

Find the exact distance between the points. See Example 1 b. Find the midpoint of the line segment whose endpoints are the given points. See Example 3 A 15, 2 12B and A, B A 17, B and A, 15B. See Example 2 See Examples 4—5 y 5 0 x 2 2 0 Objective 4: Identify x- and y-Intercepts For Exercises 45—50, estimate the x- and y-intercepts from the graph. See Example 6 A map of a wilderness area is drawn with the origin placed at the parking area. Two fire observation platforms are located at points A and B. If a fire is located at point C, determine the distance to the fire from each observation platform. A map of a state park is 5 drawn so that the origin is 4 placed at the visitor center. Suppose that 1 two hikers are located at 25 24 23 22 21 21 points A and B.

Determine the distance 23 between the hikers. If the hikers want to meet for lunch, determine the location of the midpoint between the hikers. The coordinates of the ordered pair give the number of pixels horizontally and vertically from the origin. Use this scenario for Exercises 65— Suppose that player A is located at 36, and player B is located at , How far apart are the players? Round to the nearest pixel. If the two players move directly toward each other at the same speed, where will they meet? If player A moves three times faster than player B, where will they meet? Verify that the points A 0, 0 , B x, 0 , and C a x, 2 2 make up the vertices of an equilateral triangle. Suppose that a player is located at point A , and must move in a direct line to point B 80, and then in a direct line to point C , 60 to pick up prizes before a 5-sec timer runs out. If the player moves at pixels per second, will the player have enough time to pick up both prizes? Verify that the points A 0, 0 , B x, 0 , and C 0, x make up the vertices of an isosceles right triangle an isosceles triangle has two sides of equal length.

For Exercises 69—70, assume that the units shown in the grid are in feet. Determine the exact length and width of the rectangle shown. Determine the perimeter and area. Find the center and radius of the circle. Find the area of the triangle. Assume that the units shown in the grid are in meters. Three points are collinear if they all fall on the same line. There are several ways that we can determine if three points, A, B, and C are collinear. One method is to determine if the sum of the lengths of the line segments AB and BC equals the length of AC. Suppose that d represents the distance between two points x1, y1 and x2, y2. Explain how the distance formula is developed from the Pythagorean theorem. Explain how you might remember the midpoint formula to find the midpoint of the line segment between x1, y1 and x2, y2.

Explain how to find the x- and y-intercepts from an equation in the variables x and y. Given an equation in the variables x and y, what does the graph of the equation represent? z Expanding Your Skills A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a z-axis is taken perpendicular to both the x- and y-axes. A point P is assigned an ordered triple P x, y, z relative to a fixed origin where the three axes meet. For Exercises 83—86, determine the distance between the two given points in space.

What is meant by a viewing window on a graphing device? Which of the viewing windows would show both the x- and y-intercepts of the graph of x 2 42y 5 ? See Example 7 y 5 2x 2 5 on [, 10, 1] by [, 10, 1] y 5 24x 1 1 on [, 10, 1] by [, 10, 1] y 5 x2 2 x on [25, 5, 1] by [, , ] y 5 x2 1 x on [25, 5, 1] by [, , ] For Exercises 93—94, graph the equations on the standard viewing window. Write an Equation of a Circle in Standard Form 1. Write an Equation of a Circle In addition to graphing equations by plotting points, we will learn to recognize specific categories of equations and the characteristics of their graphs. We begin by presenting the definition of a circle. in Standard Form 2.

Write the General Form of an Equation of a Circle Definition of a Circle A circle is the set of all points in a plane that are equidistant from a fixed point called the center. The fixed distance from any point on the circle to the center is called the radius. y r x, y h, k x Figure The radius of a circle is often denoted by r, where r. It is also important to note that the center is not actually part of the graph of a circle. It will be drawn in the text as an open dot for reference only. Suppose that a circle is centered at the point h, k and has radius r Figure The distance formula can be used to derive an equation of the circle. Let x, y be an arbitrary point on the circle. Then by definition the distance between h, k and x, y must be r. Apply the distance formula. EXAMPLE 1 Writing an Equation of a Circle in Standard Form a. Write the standard form of an equation of the circle with center 24, 6 and radius 2. Graph the circle. Point of Interest Solution: Among his many contributions to mathematics, René Descartes discovered analytic geometry, which uses algebraic equations to describe geometric shapes.

For example, a circle can be described by the algebraic equation x 2 h 2 1 y 2 k 2 5 r 2. Standard form: x 2 h 2 1 y 2 k 2 5 r2 Simplify. To graph the circle, first locate the center and draw a small open dot. Then plot points r units to the left, right, above, and below the center. Draw the circle through the points. Write an equation of the circle with center 3, 21 and radius 4. EXAMPLE 2 Write the standard form of an equation of the circle with endpoints of a diameter 21, 0 and 3, 4. Answers 1. Solution: 4 3 2 1 22 21 21 22 23 24 25 26 Writing an Equation of a Circle in Standard Form A sketch of this scenario is given in Figure Notice that the midpoint of the diameter is the center of the circle.

Using the endpoint 21, 0 as x1, y1 and the center 1, 2 as x2, y2 , apply the distance formula. Write the General Form of an Equation of a Circle In Example 2 we have the equation x 2 1 2 1 y 2 2 2 5 8. If we expand the binomials and combine like terms, we can write the equation in general form. x 2 1 2 1 y 2 2 2 5 8 x2 2 2x 1 1 1 y2 2 4y 1 4 5 8 x2 1 y2 2 2x 2 4y 2 3 5 0 Standard form center-radius form Expand the binomials General form General Form of an Equation of a Circle An equation of a circle written in the form x2 1 y2 1 Ax 1 By 1 C 5 0 is called the general form of an equation of a circle. By completing the square we can write an equation of a circle given in general form as an equation in standard form. The purpose of writing an equation of a circle in standard form is to identify the radius and center.

This is demonstrated in Example 3. EXAMPLE 3 Writing an Equation of a Circle in Standard Form Write the equation of the circle in standard form. Then identify the center and radius. Group the y terms. Move the constant term to the right. Complete the squares. The center is 25, 3 , and the radius is 19 5 3. Skill Practice 3 Write the equation of the circle in standard form. x2 1 y2 2 8x 1 2y 2 8 5 0 Not all equations of the form x2 1 y2 1 Ax 1 By 1 C 5 0 represent the graph of a circle. Completing the square results in an equation of the form x 2 h 2 1 y 2 k 2 5 c, where c is a constant. In the case where c. However, if c 5 0, or if c , 0, the graph will be a single point or nonexistent. These are called degenerate cases. The solution set is { h, k }.

EXAMPLE 4 Determining if an Equation Represents the Graph of a Circle Write the equation in the form x 2 h 2 1 y 2 k 2 5 r2, and identify the solution set. Note that the x2 term is already a perfect square: x 2 0 2. Complete the square: C 12 D 2 5 Since r2 5 0, the solution set is { 0, 7 }. The sum of two squares will equal zero only if each individual term is zero. Therefore, x 5 0 and y 5 7. Skill Practice 4 Write the equation in the form x 2 h 2 1 y 2 k 2 5 r2, and identify the solution set. Therefore, to graph an equation of a circle such as x 1 5 2 1 y 2 3 2 5 9, from Example 3, we first solve for y.

This is because the calculator has a rectangular screen. If the scaling is the same on the x- and y-axes, the graph will appear elongated horizontally. To eliminate this distortion, use a ZSquare option, located in the Zoom menu. Answer 4. The viewing window between x 5 These may not include x values at the leftmost and rightmost points on the circle. That is, the calculator may graph points close to 28, 3 and 22, 3 but not exactly at 28, 3 and 22, 3. Then factor the trinomial. Find the distance between 2, 3 and 23, Multiply by using the special case products.

Express your answer in simplified radical form. x 2 2 2 Concept Connections 1. A is the set of all points in a plane equidistant from a fixed point called the 2. The distance from the center of a circle to any point on the circle is called the. and is often denoted by r. The standard form of an equation of a circle with center h, k and radius r is given by 2 2 4. An equation of a circle written in the form x 1 y 1 Ax 1 By 1 C 5 0 is called the equation of a circle. form of an Objective 1: Write an Equation of a Circle in Standard Form 5. Is the point 2, 27 on the circle defined by x 1 6 2 1 y 1 1 2 5 ? For Exercises 9—16, determine the center and radius of the circle. ax 1 b 1 ay 2 b 5 7 5 9 For Exercises 17—32, information about a circle is given.

Write an equation of the circle in standard form. See Examples 1—2 Center: 22, 5 ; Radius: 1 Center: 23, 2 ; Radius: 4 Center: 24, 1 ; Radius: 3 Center: 6, 22 ; Radius: 6 Center: 24, 23 ; Radius: Center: 25, 22 ; Radius: Center: 0, 0 ; Radius: 2. Center: 0, 0 ; Radius: 4. The endpoints of a diameter are 22, 4 and 6, The endpoints of a diameter are 7, 3 and 5, The center is 22, 21 and another point on the circle is 6, 5. The center is 3, 1 and another point on the circle is 6, 5. The center is 4, 6 and the circle is tangent to the y-axis. Informally, a line is tangent to a circle if it touches the circle in exactly one point. The center is 22, 24 and the circle is tangent to the x-axis. The center is in Quadrant IV, the radius is 5, and the circle is tangent to both the x- and y-axes.

The center is in Quadrant II, the radius is 3, and the circle is tangent to both the x- and y-axes. Write an equation that represents the set of points that are 5 units from 8, Write an equation that represents the set of points that are 9 units from 24, Write an equation of the circle that is tangent to both axes with radius 17 and center in Quadrant I. Write an equation of the circle that is tangent to both axes with radius and center in Quadrant III. Determine the solution set for the equation x 1 1 2 1 y 2 5 2 5 0. Determine the solution set for the equation x 2 3 2 1 y 1 12 2 5 0.

Determine the solution set for the equation x 2 17 2 1 y 1 1 2 5 Determine the solution set for the equation x 1 15 2 1 y 2 3 2 5 For Exercises 41—54, write the equation in the form x 2 h 2 1 y 2 k 2 5 c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. See Examples 3—4 A cell tower is a site where antennas, transmitters, and receivers are placed to create a cellular network. Suppose that a cell tower is located at a point A 4, 6 on a map and its range is 1. Write an equation that represents the boundary of the area that can receive a signal from the tower. Assume that all distances are in miles. A radar transmitter on a ship has a range of 20 nautical miles. Assume that all distances on the map are represented in nautical miles. Suppose that three geological study areas are set up on a map at points A 24, 12 , B 11, 3 , and C 0, 1 , where all units are in miles. Based on the speed of compression waves, scientists estimate the distances from the study areas to the epicenter of an earthquake to be 13 mi, 5 mi, and 10 mi, respectively.

Graph three circles whose centers are located at the study areas and whose radii are the given distances to the earthquake. Then estimate the location of the earthquake. Three fire observation towers are located at points A 26, , B 14, 10 , and C 23, 13 on a map where all units are in kilometers. A fire is located at distances of 17 km, 15 km, and 13 km, respectively, from the observation towers. Graph three circles whose centers are located at the observation towers and whose radii are the given distances to the fire. Then estimate the location of the fire. Write About It State the definition of a circle. What are the advantages of writing an equation of a circle in standard form? Expanding Your Skills Find all values of y such that the distance between 4, y and 22, 6 is 10 units.

Find all values of x such that the distance between x, 21 and 4, 2 is 5 units. Find all points on the line y 5 x that are 6 units from 2, 4. Find all points on the line y 5 2x that are 4 units from 24, 6. If we solve the equation for x we get equations of the form x 5 h 6 2r 2 2 y 2 k 2. The equation x 5 h 1 2r 2 2 y 2 k 2 represents the graph of the corresponding right-side semicircle, and the equation x 5 h 2 2r 2 2 y 2 k 2 represents the graph of the left-side semicircle. These equations represent the top and bottom semicircles. For Exercises 65—68, graph the equations. Find the shortest distance from the origin to a point on the circle defined by x2 1 y2 2 6x 2 12y 1 41 5 0.

Find the shortest distance from the origin to a point on the circle defined by x2 1 y2 1 4x 2 12y 1 31 5 0. Technology Connections For Exercises 71—74, use a graphing calculator to graph the circles on an appropriate square viewing window. Determine Whether a Relation Is a Function 1. Determine Whether a In the physical world, many quantities that are subject to change are related to other variables. For example: 2. In mathematics we can express the relationship between two values as a set of ordered pairs. Definition of a Relation A set of ordered pairs x, y is called a relation in x and y. The value 8 is listed in the domain one time only. Writing a Relation from Observed Data Points Table shows the score y that a student earned on an algebra test based on the number of hours x spent studying one week prior to the test.

Write the set of ordered pairs that defines the relation given in Table Write the domain. Write the range. Hours of Study, x Test Score, y 8 92 3 58 11 98 5 72 8 86 Solution: Table a. Domain: {8, 3, 11, 5} c. Range: {92, 58, 98, 72, 86} Skill Practice 1 For the table shown, x a. Write the set of ordered pairs that defines the relation. y 3 22 5 1 24 0 3 0 The data in Table show two different test scores for 8 hr of study. That is, for x 5 8, there are two different y values. In many applications, we prefer to work with relations that assign one and only one y value for a given value of x. Such a relation is called a function. Definition of a Function Given a relation in x and y, we say that y is a function of x if for each value of x in the domain, there is exactly one value of y in the range.

EXAMPLE 2 Determining if a Relation Is a Function Determine if the relation defines y as a function of x. different y values This relation is not a function. This relation is a function. No Skill Practice 2 Determine if the relation defines y as a function of x. For example, the ordered pairs 3, 1 and 3, 24 do not make up a function. On a graph, these two points are aligned vertically. A vertical line drawn through one point also intersects the other point Figure This observation leads to the vertical line test. Using the Vertical Line Test Consider a relation defined by a set of points x, y graphed on a rectangular coordinate system.

The graph defines y as a function of x if no vertical line intersects the graph in more than one point. EXAMPLE 3 Applying the Vertical Line Test The graphs of three relations are shown in blue. In each case, determine if the relation defines y as a function of x. y y 5 4 3 2 1 In Example 3 c there is only one y value assigned to x 5 1. This is because the point 1, 2 is not included in the graph of the function as denoted by the open dot. No vertical line intersects the graph in more than one point. This is not a function. There is at least one vertical line that intersects the graph in more than one point. Skill Practice 3 Determine if the given relation defines y as a function of x. Answers 3. Yes c. No Chapter 2 Functions and Relations EXAMPLE 4 Determining if a Relation Is a Function Determine if the relation defines y as a function of x. This mapping defines the set of ordered pairs: { 1, 2 , 3, 2 , 5, 4 }. No two ordered pairs have the same x value but different y values.

y2 5 x y 5 6 1x Solve the equation for y. For any x. x 2 2 2 1 y 1 1 2 5 9 This equation represents the graph of a circle with center 2, 21 and radius 3. This relation is not a function because it fails the vertical line test. Apply Function Notation A function may be defined by an equation with two variables. For example, the equation y 5 x 2 2 defines y as a function of x. This is because for any real number x, the value of y is the unique number that is 2 less than x. When a function is defined by an equation, we often use function notation. For example, the equation y 5 x 2 2 may be written in function notation as Answers 4. Yes b. A function may be evaluated at different values of x by using substitution. f 1 5 21 can be interpreted as 1, Evaluating a Function Evaluate the function defined by g x 5 2x 1 1 for the given values of x. g 2 Solution: a. g 22 5 2 22 1 1 Substitute 22 for x. g 21 5 2 21 1 1 Substitute 21 for x. However, lowercase letters such as f, g, h, and so on are often used.

g 2 5 5 The function values represent the ordered pairs 22, 23 , 21, 21 , 0, 1 , 1, 3 , and 2, 5. The line through the points represents all ordered pairs defined by this function. This is the graph of the function. h 21 EXAMPLE 6 c. h 3 Evaluating a Function Evaluate the function defined by f x 5 3x2 1 2x for the given values of x. f x 1 h Solution: a. Substitute a for x. Skill Practice 6 Evaluate the function defined by f x 5 2x2 1 4x for the given values of x. f a 1 h Chapter 2 Functions and Relations 3. Determine x- and y-Intercepts of a Function Defined by y 5 f x Recall that to find an x-intercept s of the graph of an equation, we substitute 0 for y in the equation and solve for x.

Using function notation, y 5 f x , this is equivalent to finding the real solutions of the equation f x 5 0. To find the y-intercept, substitute 0 for x and solve the equation for y. Using function notation, this is equivalent to finding f 0. EXAMPLE 7 Finding the x- and y-Intercepts of a Function Find the x- and y-intercepts of the function defined by f x 5 x2 2 4. Solution: To find the x-intercept s , solve the equation f x 5 0. To find the y-intercept, evaluate f 0. Skill Practice 7 Find the x- and y-intercepts of the function defined by f x 5 0 x 0 2 5. Determine Domain and Range of a Function Given a relation defining y as a function of x, the domain is the set of x values in the function, and the range is the set of y values in the function. In Example 8, we find the domain and range from the graph of a function. EXAMPLE 8 Determining Domain and Range Determine the domain and range for the functions shown. f x 23 Answer 7. x-intercepts: 5, 0 and 25, 0 ; y-intercept: 0, 25 24 25 c.

The graph defines the set of ordered pairs: { 23, 24 , 21, 3 , 0, 1 , 2, 4 , 4, 4 } Domain: {23, 21, 0, 2, 4} Range: {24, 1, 3, 4} The domain is the set of x values. The range is the set of y values. Domain: {x 0 x. Range: {y 0 y. h x 5 4 3 2 The graph extends infinitely far downward and infinitely far to the left and right. Therefore, the domain is the set of all real numbers, x. If no such restriction is stated, then by default, the domain is all real numbers that when substituted into the function produce real numbers in the range. Guidelines to Find Domain of a Function To determine the implied domain of a function defined by y 5 f x , Answers 8. Domain: {24, 22, 0, 3, 4}; Range: {23, 0, 1, 5} b. x x13 b. h t 5 12 2 t Solution: The domain is all real numbers except those that make the denominator zero. Therefore, x2 1 4. Denominator always positive never zero c. g x 5 x x13 2x 2 5 The variable x has the restriction that 2x 2 5? Therefore, x?

f x 5 The domain is restricted to the real numbers that make the radicand greater than or equal to zero. Divide by 21 and reverse the inequality sign. The expression 0 4 1 a 0 is a real number for all real numbers a. Skill Practice 9 Write the domain of each function in interval notation. Interpret a Function Graphically In Example 10, we will review the key concepts studied in this section by identifying characteristics of a function based on its graph. EXAMPLE 10 Identifying Characteristics of a Function Use the function f pictured to answer the questions.

Answers 9. Determine f 2. Determine f Find all x for which f x 5 0. Find all x for which f x 5 3. Determine the x-intercept s. Determine the y-intercept. Determine the domain of f. Determine the range of f. f 25 is not defined. f 2 5 5 because the function contains the point 2, 5. The point 25, 23 is not included in the function as indicated by the open dot. The points 24, 0 and 4, 0 represent the points where f x 5 0. f x 5 3 for all x on the interval [23, 1] and for x 5 The x-intercepts are 24, 0 and 4, 0. The y-intercept is 0, 3.

Skill Practice 10 a. Answers All x on the interval [23, 21] e. The x-intercept s. The y-intercept. The domain of f. The range of f. f x 5 4 3 2 y 5 f x 1 25 24 23 22 21 21 22 1 2 3 4 5 x 23 24 25 Practice Exercises Prerequisite Review R. Solve the equation using the square root property. Write the solution set in interval notation. Given 2x 2 5y 5 20, a. Find the x-intercept. Find the y-intercept. Concept Connections 1. Given a function defined by y 5 f x , the statement f 2 5 4 is equivalent to what ordered pair? x11 5. Given f x 5 , the domain is restricted so that x? x15 6. Consider a relation that defines the height y of a tree for a given time t after it is planted. Does this relation define y as a function of t?

Consider a relation that defines a time y during the course of a year when the temperature T in Fort Collins, Colorado, is Does this relation define y as a function of T? Write a set of ordered pairs x, y that defines the relation. Write the domain of the relation. Write the range of the relation. Determine if the relation defines y as a function of x. See Examples 1—2 9. Number of Oscar Nominations y Actor x Elevation at Airport ft y City x 5 Albany 12 Denver Sean Penn 5 Miami 11 Dustin Hoffman 7 San Francisco 11 Tom Hanks Jack Nicholson y Answer true or false. All relations are functions. All functions are relations. For Exercises 15—32, determine if the relation defines y as a function of x. See Examples 3—4 y y 5 x 2 4 Functions and Relations x 5 0 y 0 Objective 2: Apply Function Notation The statement f 4 5 1 corresponds to what ordered pair? The statement g 7 5 25 corresponds to what ordered pair?

For Exercises 35—56, evaluate the function for the given value of x. gA B d. h 27 gA 13 B k 25 f 25 k g x 1 h For Exercises 57—62, find and simplify f x 1 h. Determine f 9. Determine f 3. For what value of x is f x 5 6? For what value of x is f x 5 7? For what value of x is f x 5 3? For what value of x is f x 5 4? Joe rides his bicycle an average of 18 mph. The distance Joe rides d t in mi is given by d t 5 18t, where t is the time in hours that he rides. Evaluate d 2 and interpret the meaning. Determine the distance Joe travels in 40 min.

Frank needs to drive mi from Daytona Beach to Miami. After having driven x miles, the distance remaining r x in mi is given by r x 5 2 x. Evaluate r 50 and interpret the meaning. Determine the distance remaining after mi. At a restaurant, if a party has eight or more people, the gratuity is automatically added to the bill. Evaluate C and interpret the meaning in the context of this problem. Evaluate P 60 and interpret the meaning in the context of this problem. A student decides to finance a used car over a 5-yr month period. Determine the t-intercept and y-intercept and interpret their meanings in context. The amount spent on video games per person in the United States has been increasing since Source: www.

gov The function defined by f x 5 9. Determine the y-intercept and interpret its meaning in context. See Example 8 y y Functions and Relations y See Example 9 h a 5 5 8 1 Za 2 2Z 1 2 t 1 3 1 t25 1 5 1 x23 2 Chapter 2 Functions and Relations n x 5 3x 2 7; 22 , x , 2 Objective 5: Interpret a Function Graphically For Exercises —, use the graph of y 5 f x to answer the following. See Example 10 a. Find all x for which f x 5 y Suppose that a phone card has min. Write a relationship that represents the number of minutes remaining r x as a function of the number of minutes already used x.

Suppose that a roll of wire has ft. Write a relationship that represents the amount of wire remaining w x as a function of the number of feet of wire x already used. Given an equilateral triangle with sides of length x, write a relationship that represents the perimeter P x as a function of x. In an isosceles triangle, two angles are equal in measure. If the third angle is x degrees, write a relationship that represents the measure of one of the equal angles A x as a function of x. Two adjacent angles form a right angle.

If the measure of one angle is x degrees, write a relationship representing the measure of the other angle C x as a function of x. Two adjacent angles form a straight angle If the measure of one angle is x degrees, write a relationship representing the measure of the other angle S x as a function of x. Write a relationship for a function whose f x values are 2 less than three times the square of x. Write a relationship for a function whose f x values are 3 more than the principal square root of x. If two points align vertically then the points do not define y as a function of x. Explain why.

Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them. To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzed reviews to verify trustworthiness. close ; } } this. getElementById iframeId ; iframe. max contentDiv. scrollHeight, contentDiv. offsetHeight, contentDiv. document iframe. When Julie Miller began writing her successful developmental math series one of her primary goals was to bridge the gap between preparatory courses and college algebra. With the Miller College Algebra series Julie has carried forward her clear concise writing style; highly effective pedagogical features; and complete author-created technological package to students in this course area. Previous page. Sticky notes.

On Kindle Scribe. McGraw-Hill Higher Education. Publication date. January 8, File size. See all details. Next page. Due to its large file size, this book may take longer to download. Kindle e-Readers Kindle 5th Generation Kindle Keyboard Kindle DX Kindle 2nd Generation Kindle 1st Generation Kindle Paperwhite Kindle Paperwhite 5th Generation Kindle Touch Kindle Voyage Kindle Kindle Oasis. Fire Tablets Kindle Fire HDX 8. Fire Phones Fire Phone. Free Kindle Reading Apps Kindle for Windows 8 Kindle for Windows Phone Kindle for BlackBerry Kindle for Android Phones Kindle for Android Tablets Kindle for iPhone Kindle for iPod Touch Kindle for iPad Kindle for Mac Kindle for PC Kindle Cloud Reader. Customers who viewed this item also viewed.

Page 1 of 1 Start over Page 1 of 1. College Algebra. James Stewart. Kindle Edition. College Algebra DeMYSTiFieD, 2nd Edition. Rhonda Huettenmueller. Jay Abramson. Julie Miller. Mastering Algebra - Advanced Level: Over 2, Solved Problems Hamilton Education Guides Book 4. Dan Hamilton. Robert F. About the Author Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers.

My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. Brief content visible, double tap to read full content. Full content visible, double tap to read brief content. Help others learn more about this product by uploading a video! About the author Follow authors to get new release updates, plus improved recommendations. Discover more of the author’s books, see similar authors, read author blogs and more. Read more Read less. Customer reviews. How customer reviews and ratings work Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them. Learn more how customers reviews work on Amazon.

Images in this review. Reviews with images. See all customer images. Top reviews Most recent Top reviews. Top reviews from the United States. There was a problem filtering reviews right now. Please try again later. Verified Purchase. It’s a good quality math book. It’s held up all semester and makes it easy to follow along with my class. Product was in good condition no rips and tears, came fairly quickly, did not come with access code because I rented the book, and there was no writing on it. Easy to use and navigate through online. This was a book my son needed for a college course. This program saved money. Good shape, exactly what I needed. Great condition and welcome alternative to buying overpriced college books.

This book is hard to read. I thought it would help with my online class and it was no help at all. pages have info all over them tips in little boxes like tips, objectives, avoiding mistakes and lots of examples but explanations were lacking, the "why" was what I was looking for and it isn't here. Even pages without tips had the huge wasted empty space. Glad it was a rental not a purchase. See all reviews. Report an issue. Does this item contain inappropriate content? Do you believe that this item violates a copyright? Does this item contain quality or formatting issues? Your recently viewed items and featured recommendations. Back to top. Get to Know Us. Make Money with Us. Amazon Payment Products. Let Us Help You. Conditions of Use Privacy Notice Interest-Based Ads © , Amazon.

com, Inc. or its affiliates. Amazon Music Stream millions of songs. Amazon Advertising Find, attract, and engage customers. Amazon Drive Cloud storage from Amazon. ACX Audiobook Publishing Made Easy. Sell on Amazon Start a Selling Account. Amazon Business Everything For Your Business. AmazonGlobal Ship Orders Internationally. Home Services Experienced Pros Happiness Guarantee. Amazon Ignite Sell your original Digital Educational Resources. Amazon Web Services Scalable Cloud Computing Services.

College algebra 2nd edition julie miller pdf download-1st,Book Preface

Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to Click Done and download the resulting document. Our solution allows you to take the whole process of executing legal forms online. As a result, you save hours (if not days or weeks) and View PDF Textbooks: College Algebra, by Julie Miller, 2nd edition. Technology: A TI 83+, or an equivalent graphing calculator, is required. View PDF 2. Register with your SFA email and College Algebra 2nd Edition is written by Julie Miller and published by McGraw-Hill Higher Education. The Digital and eTextbook ISBNs for College Algebra are , College Algebra (Collegiate Math) 2nd Edition, Julie Miller Buy launch College Algebra (Collegiate Math) 2nd Edition Julie Miller, Donna Gerken Publisher: McGraw-Hill Education Oct 15,  · Julie Miller Daytona State College Digital contributions from Donna Gerken Miami-Dade College Kendall COLLEGE ALGEBRA, SECOND EDITION Published by McGraw-Hill ... read more

For example, if a y-intercept is 0, 2 , then it may be stated simply as 2. Apply the Point-Slope Formula 1. Skill Practice 6 Given the equation y 5 x2 2 4, a. Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. The value of x is the month number and x 5 1 represents January.

All functions are relations. An x-intercept of a graph has a y-coordinate of. Page 1 of 1 Start over Page 1 of 1. Two key features are the x- and y-intercepts of a graph. Thank you for overseeing the enormous job of managing digital content and ensuring consistency of the author voice. College algebra 2nd edition julie miller pdf download exact distance is 4 units. Your text has great instructor tools, like presentation slides, instructor manuals, test banks and more.