Unit 6: Absolute Value
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1 Algebra 1 NAME: Unit 6: Absolute Value Note Packet Date Topic/Assignment HW Page 6-A Introduction to Absolute Value Functions 6-B Reflections of Absolute Value Functions 6-C Solve Absolute Value Equations 6-D Solve Absolute Value Equations by Graphing 6-E Exploring a Values of Absolute Value Functions 6-F Stretching and Compressing Absolute Value Functions 6-G Graphing Absolute Value Functions Activity Review Test Due Date Score (For Teacher Use Only) 1
2 Warm-Up Warm-Up Warm-Up Solve the systems. 2
3 Warm-Up Solve the following equation or inequality. a xx 4 = 3 10 b. 2xx + 5 < 13 Warm-Up Graph each line. 3
4 Warm-Up Use the graphs to fill in the information. Warm-Up Warm-Up Solve the equation and inequality. 4
5 Warm-Up Warm-Up Warm-Up Warm-Up Write the equation of the line with slope m = 2/3 through the point (6, -9). 5
6 6-A: Introduction to Absolute Value Functions Opener: What does absolute value mean? Evaluate each: a. 2 b. 2 c. 2 d. 2 8 e. 2 8 Absolute Value Functions 1. Example Graph each by plotting points. a. ff(xx) = xx b. ff(xx) = xx 2 c. ff(xx) = xx + 1 Write a rule to describe the pattern you notice: 6
7 2. Example Graph each by plotting points. a. yy = xx + 2 b. yy = xx 1 c. yy = xx 3 Write a rule to describe the pattern you notice: ff(xx) = ±aa xx h + kk Vertex: 3. Example Find the vertex of each, then graph. a. yy = xx b. yy = xx 4 2 c. yy = xx
8 4. Guided Practice. Find the vertex of each, then graph. a. yy = xx 2 4 b. yy = xx c. yy = xx Example. Graph each with the given domain. a. yy = xx 3 b. yy = xx 1 c. yy = xx ffffff xx < 2 ffffff xx 3 ffffff 3 xx < 2 6. Guided Practice. Graph each with the given domain. a. yy = xx + 2 b. yy = xx + 1 c. yy = xx 1 2 ffffff xx < 2 ffffff xx 3 ffffff 3 xx < 2 8
9 6-B: Reflections of Absolute Value Functions Evaluate each. a. 3 b. 3 c. 3 d. 3 Graph each and compare. ff(xx) = xx ff(xx) = xx ff(xx) = ±aa xx h + kk 1. Example Graph each. a. yy = xx b. yy = xx c. yy = xx
10 2. Guided Practice Graph each. a. yy = xx b. yy = xx 3 1 c. yy = xx Example State the domain and range of each. a. b. c. 4. Guided Practice a. b. c. 10
11 5. Example Write the equation for the graph shown. a. b. c. 6. Guided Practice a. b. c. 11
12 6-C: Solving Absolute Value Equations Absolute Value Definition xx = 3 1. Example Solve each equation. a. xx + 1 = 5 b. xx 2 1 = 5 c. 2xx 9 = 3 d. 3xx = 5 e. 2xx = 11 f. 2xx 1 = 5 Steps for solving absolute value equations: When will the answer be no solution? 12
13 2. Guided Practice Solve each. a. xx 2 = 6 b. xx = 4 c. 3xx + 10 = 2 d. 2xx 1 12 = 6 e. 4xx = 11 f. 3xx 2 4 = 5 3. Example Solve each. a. 2 2xx + 1 = 10 b. xx = 5 c. 2 2xx = 3 4. Guided Practice Solve each. d. 3 3xx = 8 e. 2xx = 8 f. 2xx = 5 13
14 6-D: Solve Absolute Value Equations by Graphing Opener: Graph the absolute value equation yy = xx and the linear equation yy = 1 on the same grid. Identify the ordered pairs where the two graphs INTERSECT: Identify the x-values of those ordered pairs: 1. Example Solve by graphing. a. xx 1 3 = 2 b. xx = 4 c. xx = 4 Solution: Solution: Solution: How to solve by graphing: 14
15 2. Guided Practice. Solve by graphing. a. xx = 1 b. xx 1 3 = 2 c. xx = 4 Solution: Solution: Solution: 3. Example Graph the absolute value over the given domain. a. yy = xx b. yy = xx 2 3 c. yy = xx + 4 ffffff 4 xx < 2 ffffff xx < 5 ffffff xx 2 15
16 4. Guided Practice. Graph the absolute value function over the given domain. a. yy = xx b. yy = xx + 1 c. yy = xx 5 ffffff 5 < xx < 3 ffffff xx 2 ffffff xx < 3 5. Guided Practice. Write the equation for the graph shown. a. b. 16
17 6-E: Exploring a Values of Absolute Value Functions Opener: 1. 1a. Describe what is happening to the y-values of g(x) compared to f(x) at the same x-values: 1b. Describe how the graph of gg(xx) = 2 xx compares with the graph of ff(xx) = xx. Use either the word stretch or shrink and include the direction of momement. 1c. What other transformation occurs when the value of aa in gg(xx) = aa xx is negative? 17
18 2. 18
19 6-F: Stretching and Compressing Absolute Value Functions yy = ±aa xx h + kk To graph absolute value functions when a is other than 1: 1. Example Graph each. a. ff(xx) = 2 xx 1 3 b. ff(xx) = 3 xx c. ff(xx) = 2 xx Guided Practice a. ff(xx) = 1 xx 4 b. ff(xx) = 3 xx + 2 c. ff(xx) = 4 xx
20 3. Example Graph each. a. ff(xx) = 1 xx + 2 b. ff(xx) = 3 xx + 1 c. ff(xx) = 4 xx Dom: Dom: Dom: Rng: Rng: Rng: 4. Guided Practice a. ff(xx) = 2 xx + 4 b. ff(xx) = 2 xx c. ff(xx) = 1 xx Dom: Dom: Dom: Rng: Rng: Rng: 20
21 5. Example Write the equation for the graph shown. a. b. 6. Guided Practice Write the equation for the graph shown or described. a. b. c. Reflect the parent function ff(xx) = xx across the x- axis, stretch it by a factor of 4 3, and shift it three units up and one unit to the left. d. This one has a specific domain. 21
22 6-G: Graphing Absolute Value Functions Activity Your teacher will give your group one large grid on which you ll graph your function. 22
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