Download presentation

Presentation is loading. Please wait.

Published byVerity Wheeler Modified over 2 years ago

1
Appendices © 2008 Pearson Addison-Wesley. All rights reserved

2
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-2 Appendices Appendix AEquations and Inequalities Appendix BGraphs of Equations Appendix CFunctions Appendix DGraphing Techniques

3
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-3 Equations and Inequalities A Equations ▪ Solving Linear Equations ▪ Solving Quadratic Equations ▪ Inequalities ▪ Solving Linear Inequalities ▪ Interval Notation ▪ Three-Part Inequalities

4
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-4 A Example 1 Solving a Linear Equation (page 423) Solve. Solution set: {6} Distributive property Combine terms. Add 4 to both sides. Add 12x to both sides. Combine terms. Divide both sides by 4.

5
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-5 Solve. A Example 2 Clearing Fractions Before Solving a Linear Equation (page 424) Solution set: {–10} Multiply by 10, the LCD of all the fractions. Distributive property Combine terms. Add –4s and –6 to both sides. Combine terms. Divide both sides by –6.

6
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-6 Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. A Example 3(a) Identifying Types of Equations (page 425) This is a conditional equation. Solution set: {11} Add –4x and 9 to both sides. Combine terms. Divide both sides by 2.

7
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-7 Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. This is a contradiction. Solution set: ø Distributive property Subtract 14x from both sides. A Example 3(b) Identifying Types of Equations (page 425)

8
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-8 Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. A Example 3(c) Identifying Types of Equations (page 425) This is an identity. Solution set: {all real numbers} Distributive property Combine terms. Add x and –3 to both sides.

9
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-9 A Example 4 Using the Zero-Factor Property (page 426) Solve. Factor. Set each factor equal to 0 and then solve for x. or

10
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-10 A Example 4 Using the Zero-Factor Property (cont.) Now check. Solution set:

11
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-11 A Example 5 Using the Square Root Property (page 426) Solve each quadratic equation. Generalized square root property (a) (b)

12
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-12 A Example 6 Using the Quadratic Formula (Real Solutions) (page 115) Solve. a = 1, b = 6, c = –3 Write the equation in standard form. Quadratic formula

13
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-13 A Example 6 Using the Quadratic Formula (Real Solutions) (cont.) Solution set:

14
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-14 Subtract 7. Divide by –2. Reverse the direction of the inequality symbol when multiplying or dividing by a negative number. Solution set: {x|x > 6} A Example 7 Solving a Linear Inequality (page 428) Solve.

15
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-15 A Example 8 Solving a Three-Part Inequality (page 429) Solve. Add 8. Divide by 6. Solution set:

16
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-16 Graphs of Equations B The Rectangular Coordinate System ▪ The Pythagorean Theorem and the Distance Formula ▪ The Midpoint Formula ▪ Graphing Equations ▪ Circles

17
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-17 B Example 1 Using the Distance Formula (page 433) Find the distance between P(3, –5) and Q(–2, 8). The distance between P(3, –5) and Q(–2, 8) is

18
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-18 Find the coordinates of the midpoint M of the segment with endpoints (–7, –5) and (–2, 13). B Example 2 Using the Midpoint Formula (page 434) Midpoint formula: The coordinates of the midpoint M of the segment with endpoints (–7, –5) and (–2, 13) are

19
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-19 B Example 3(a) Finding Ordered Pairs That are Solutions to Equations (page 434) x –1–1 1 3 Three ordered pairs that are solutions are (−1, 7), (1, 3), and (3, −1). Find three ordered pairs that are solutions to y = –2x + 5.

20
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-20 Find three ordered pairs that are solutions to. B Example 3(b) Finding Ordered Pairs That are Solutions to Equations (page 434) x –2–2 –1–1 2 Three ordered pairs that are solutions are (−2, −3), (−1, 0), and (2, −3).

21
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-21 B Example 4(a) Graphing Equations (page 435) Step 1: Find the x-intercept and the y-intercept. Intercepts: and Graph the equation y = –2x + 5. (See Classroom Example 3a.)

22
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-22 B Example 4(a) Graphing Equations (cont.) Step 2: Use the other ordered pairs found in Example 3a: (−1, 7), (1, 3), and (3, −1). Steps 3 and 4: Plot and then connect the five points.

23
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-23 Graph the equation. (See Classroom Example 3b.) B Example 4(b) Graphing Equations (page 435) Step 1: Find the x-intercept and the y-intercept. Intercepts: (–1, 0), (1, 0) and (0, 1)

24
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-24 B Example 8(c) Graphing Equations (cont.) Step 2: Use the other ordered pairs found in Example 3b: (−2, −3) and (2, −3). Steps 3 and 4: Plot and then connect the five points.

25
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-25 Find the center-radius form of the equation of each circle described. B Example 5 Find the Center-Radius Form (page 437) (a) Center at (1, –2), radius 3 (b) Center at (0, 0), radius 2 (h, k) = (1, –2), r = 3 (h, k) = (0, 0), r = 2

26
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-26 B Example 6(a) Graphing Circles (page 437) Graph Write the equation as (h, k) = (1, –2), r = 3

27
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-27 B Example 6(b) Graphing Circles (page 437) Graph (h, k) = (0, 0), r = 2 Write the equation as

28
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-28 Functions C Relations and Functions ▪ Domain and Range ▪ Determining Functions from Graphs or Equations ▪ Function Notation ▪ Increasing, Decreasing, and Constant Functions

29
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-29 C Example 1 Deciding Whether Relations Define Functions (page 441) Decide whether the relation determines a function. M is a function because each distinct x-value has exactly one y-value. (a)

30
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-30 C Example 1 Deciding Whether Relations Define Functions (cont.) (b) N is not a function because the x-value –4 has two y-values.

31
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-31 Give the domain and range of the relation. Is the relation a function? {(–4, – 2), ( – 1, 0), (1, 2), (3, 5)} Domain: {–4, – 1, 0, 3} Range: {–2, 0, 2, 5} The relation is a function because each x-value corresponds to exactly one y-value. C Example 2(a) Finding Domains and Ranges of Relations (page 442)

32
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-32 C Example 2(b) Finding Domains and Ranges of Relations (cont.) Give the domain and range of the relation. Is the relation a function? Domain: {1, 2, 3} Range: {4, 5, 6, 7} The relation is not a function because the x-value 2 corresponds to two y-values, 5 and 6.

33
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-33 C Example 3(a) Finding Domains and Ranges from Graphs (page 442) Give the domain and range of the relation. Domain: {–2, 4} Range: {0, 3}

34
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-34 C Example 3(b) Finding Domains and Ranges from Graphs (cont.) Give the domain and range of the relation. Domain: Range:

35
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-35 Give the domain and range of the relation. Domain: [–5, 5] Range: [–3, 3] C Example 3(c) Finding Domains and Ranges from Graphs (cont.)

36
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-36 C Example 3(d) Finding Domains and Ranges from Graphs (cont.) Give the domain and range of the relation. Domain: Range:

37
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-37 Determine if the relation is a function and give the domain and range. y is found by multiplying x by 2 and subtracting 5. C Example 4(a) Identifying Functions, Domains, and Ranges (page 444) y = 2x – 5 Domain: Range: Each value of x corresponds to just one value of y, so the relation is a function.

38
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-38 Determine if the relation is a function and give the domain and range. y is found by squaring x by 2 and adding 3. C Example 4(b) Identifying Functions, Domains, and Ranges (cont.) y = x 2 + 3 Domain: Range: Each value of x corresponds to just one value of y, so the relation is a function.

39
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-39 Determine if the relation is a function and give the domain and range. For any choice of x in the domain, there are two possible values for y. C Example 4(c) Identifying Functions, Domains, and Ranges (cont.) x = |y| Domain: Range: The relation is not a function.

40
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-40 Determine if the relation is a function and give the domain and range. y is found by dividing 3 by x + 2. C Example 4(d) Identifying Functions, Domains, and Ranges (cont.) Domain: Range: Each value of x corresponds to just one value of y, so the relation is a function.

41
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-41 Let and. Find f(–3), f(r), and g(r + 2). C Example 5 Using Function Notation (page 445)

42
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-42 Find f(–1) for each function. (a) f(x) = 2x 2 – 9 (b) f = {(–4, 0), (–1, 6), (0, 8), (2, –2)} C Example 6 Using Function Notation (page 446) f(–1) = 2( – 1) 2 – 9= –7 f( – 1) = 6

43
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-43 Find f(–1) for each function. (c)(d) C Example 6 Using Function Notation (cont.) f(–1) = 5f( – 1) = 0

44
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-44 The figure is the graph of a function. Determine the intervals over which the function is increasing, decreasing, or constant. C Example 7 Determining Intervals Over Which a Function is Increasing, Decreasing, or Constant (page 447) Increasing onDecreasing on Constant on

45
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-45 Graphing Techniques D Stretching and Shrinking ▪ Reflecting ▪ Symmetry ▪ Translations

46
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-46 D Example 1 Stretching or Shrinking a Graph (page 451) x –2–2 –1–1 0 1 2 41 1 ¼ 00 1 ¼ 41 Create a table of values. Note that for corresponding values of x, the y-values of g(x) are each one-fourth that of f(x). Graph the function

47
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-47 D Example 2 Reflecting a Graph Across an Axis (page 452) x –2–2 –1–1 0 1 2 2–2–2 1–1 00 1 –1–1 2–2 Create a table of values. Note that every y-value of g(x) is the negative of the corresponding y-value of f(x). The graph of f(x) is reflected across the x-axis to give the graph of g(x). Graph the function

48
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-48 D Example 2 Reflecting a Graph Across an Axis (cont.) x –2–2 –1–1 0 1 2 22 11 00 1 1 22 Create a table of values. Note that every y-value of g(x) is the same of the corresponding y-value of f(x). The graph of f(x) is reflected across the y-axis to give the graph of g(x). Graph the function

49
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-49 D Example 3(a) Testing for Symmetry with Respect to an Axis (page 454) Test for symmetry with respect to the x-axis and the y-axis. Replace x with –x: The result is not the same as the original equation. The graph is not symmetric with respect to the y-axis. Replace y with –y: The result is the same as the original equation. The graph is symmetric with respect to the x-axis. The graph is symmetric with respect to the x-axis only.

50
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-50 D Example 3(a) Testing for Symmetry with Respect to an Axis (cont.)

51
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-51 D Example 3(b) Testing for Symmetry with Respect to an Axis (page 454) Test for symmetry with respect to the x-axis and the y-axis. Replace x with –x: The result is the same as the original equation. The graph is symmetric with respect to the y-axis. Replace y with –y: The result is the not same as the original equation. The graph is not symmetric with respect to the x-axis. The graph is symmetric with respect to the y-axis only.

52
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-52 D Example 3(b) Testing for Symmetry with Respect to an Axis (cont.)

53
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-53 D Example 3(c) Testing for Symmetry with Respect to an Axis (page 454) Test for symmetry with respect to the x-axis and the y-axis. Replace x with –x: The result is not the same as the original equation. The graph is not symmetric with respect to the y-axis. Replace y with –y: The result is the not same as the original equation. The graph is not symmetric with respect to the x-axis. The graph is not symmetric with respect to either axis.

54
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-54 D Example 3(c) Testing for Symmetry with Respect to an Axis (cont.)

55
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-55 D Example 3(d) Testing for Symmetry with Respect to an Axis (page 454) Test for symmetry with respect to the x-axis and the y-axis. Replace x with –x: The result is the same as the original equation. The graph is symmetric with respect to the y-axis. Replace y with –y: The result is same as the original equation. The graph is symmetric with respect to the x-axis. The graph is symmetric with respect to both axes.

56
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-56 D Example 3(d) Testing for Symmetry with Respect to an Axis (cont.)

57
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-57 D Example 4(a) Testing for Symmetry with Respect to the Origin (page 455) Is the graph of symmetric with respect to the origin? Replace x with –x and y with –y: The result is the same as the original equation. The graph is symmetric with respect to the origin.

58
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-58 D Example 4(b) Testing for Symmetry with Respect to the Origin (page 455) ) Is the graph of symmetric with respect to the origin? Replace x with –x and y with –y: The result is not the same as the original equation. The graph is not symmetric with respect to the origin.

59
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-59 D Example 5(a) Translating Graphs (page 455) Graph. Compare a table of values for with. x –2–2 –1–1 0 1 2 46 13 02 13 46 The graph of f(x) is the same as the graph of g(x) translated 2 units up.

60
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-60 D Example 5(b) Translating Graphs (page 455) Graph. x –4–4 –3–3 –2 –2 –1 –1 0 1 164 91 40 11 04 Compare a table of values for with. 19

61
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-61 D Example 5(b) Translating Graphs (cont.) Graph. The graph of f(x) is the same as the graph of g(x) translated 2 units left.

62
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendices-62 D Example 6 Using More Than One Transformation on a Graph (page 457) Graph. This is the graph of translated one unit to the right, reflected across the x-axis, and then translated four units up.

Similar presentations

OK

Review for EOC Algebra. 1) In the quadratic equation x² – x + c = 0, c represents an unknown constant. If x = -4 is one of the solutions to this equation,

Review for EOC Algebra. 1) In the quadratic equation x² – x + c = 0, c represents an unknown constant. If x = -4 is one of the solutions to this equation,

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Hrm ppt on recruitment matters Ppt on abstract art gallery Ppt on laser power transmission Ppt on allotropes of carbon Ppt on net etiquettes of life Free ppt on moving coil galvanometer experiment Ppt on basics of ms word 2007 Ppt on ideal gas law equation Ppt on wild animals in india 3d holographic display ppt on tv