2-7 Parent Functions and Transformations. Identify the type of function represented by each graph. ANSWER: linear ANSWER: absolute value
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1 Identify the type of function represented by each graph. 4. translation of the graph of y = x left 1 unit 1. linear Describe the reflection in each function. Then 5. reflection of the graph of across the x-axis 2. absolute value CCSS SENSE-MAKING Describe the translation in each function. Then graph the function. 3. translation of the graph of y = x 2 down 4 units 6. reflection of the graph of y = x 2 across the y-axis esolutions Manual - Powered by Cognero Page 1
2 7. Describe the dilation in each function. Then A vertical compression of the graph of y = x ; the slope is not as steep as that of y = x. 9. FOOD The manager of a coffee shop is randomly checking cups of coffee drinks prepared by employees to ensure that the correct amount of coffee is in each cup. Each 12-ounce drink should contain half coffee and half steamed milk. The amount of coffee by which each drink varies can be represented by Describe the transformations in the function. Then The function is a dilation and translation. The graph of right. compresses the graph vertically and translates it 12 units to the 8. The dilation stretches the graph of y = x 2 vertically. Identify the type of function represented by each graph. 10. constant esolutions Manual - Powered by Cognero Page 2
3 Describe the translation in each function. Then translation of the graph of y = x 2 up 4 units quadratic 12. absolute value 15. translation of the graph of y = x down 3 units 13. linear 16. translation of the graph of y = x down 1 unit or right 1 unit esolutions Manual - Powered by Cognero Page 3
4 17. translation of the graph of y = x up 2 units or left 2 units 20. Describe the reflection in each function. Then reflection of the graph of y = x across the x-axis 18. translation of the graph of y = x 2 right 5 units 21. reflection of the graph of y = x 2 across the x-axis translation of the graph of y = x left 6 units reflection of the graph of y = x 2 across the y-axis esolutions Manual - Powered by Cognero Page 4
5 23. Describe the dilation in each function. Then reflection of the graph of across the y-axis 26. horizontal compression of the graph of y = x reflection of the graph of across the x-axis 27. vertical compression of the graph of y = x; The slope is steeper than that of y = x. 25. reflection of the graph of y = x across the y-axis 28. The dilation stretches the graph of vertically. esolutions Manual - Powered by Cognero Page 5
6 29. The dilation compressed the graph of horizontally. 32. CCSS SENSE-MAKING A non-impact workout can burn up to 7.5 Calories per minute. The equation to represent how many Calories a person burns after m minutes of the workout is C(m) = 7.5m. Identify the transformation in the function. Then The graph is a dilation of the graph of y = x. The dilation stretches the graph vertically. 30. The dilation compressed the graph of y = x vertically; the slope is not as steep as that of y = x. Write an equation for each function vertical compression of the graph of y = x 2 esolutions Manual - Powered by Cognero Page 6
7 y = (x 2) y = x BUSINESS The graph of the cost of producing x widgets is represented by the blue line in the graph. After hiring a consultant, the cost of producing x widgets is represented by the red line in the graph. Write the equations of both lines and describe the transformation from the blue line to the red line. 36. Blue: y = x + 4; red: y = x + 2; the red line is a translation of the blue line 2 units down. esolutions Manual - Powered by Cognero Page 7
8 40. ROCKETRY Kenji launched a toy rocket from ground level. The height h(t) of Kenji s rocket after t seconds is shown in blue. Emily believed that her rocket could fly higher and longer than Kenji s. The flight of Emily s rocket is shown in red. Write an equation for each function. a. Identify the type of function shown. b. How much longer than Kenji s rocket did Emily s rocket stay in the air? 41. c. How much higher than Kenji s rocket did Emily s rocket go? d. Describe the type of transformation between the two graphs. 42. a. quadratic b. about 1.5 seconds c. about 25 ft higher d. a dilation in which the red graph is an expansion of the blue graph 43. CHALLENGE Explain why performing a horizontal translation followed by a vertical translation ends up being the same transformation as performing a vertical translation followed by a horizontal translation. Sample answer: Since a vertical translation concerns only y-values and a horizontal translation concerns only x-values, order is irrelevant. esolutions Manual - Powered by Cognero Page 8
9 44. CCSS CRITIQUE Carla and Kimi are determining if f (x) = 2x is the identity function. Is either of them correct? Explain your reasoning. 47. WRITING IN MATH Explain why the reflection of the graph of f (x) = x 2 in the y-axis is the same as the graph of f (x) = x 2. Is this true for all reflections of quadratic equations? If not, describe a case when it is false. Kimi; Sample answer: Linear equations that go through the origin are not always the identity. The identity linear function is f (x) = x. 45. OPEN ENDED Draw a figure in Quadrant II. Use any of the transformations you learned in this lesson to move your figure to Quadrant IV. Describe your transformation. Sample graph: Sample answer: It is not always true. When the axis of symmetry of the parabola is not along the y-axis, the graphs of the preimage and image will be different. 48. What is the solution set of the inequality? A B C D D Sample answer: The figure in Quadrant II has been reflected and moved right 10 units. 46. REASONING Study the parent graphs at the beginning of this lesson. Select a parent graph with positive y-values at its leftmost points and positive y- values at its rightmost points. Sample answer: The graph of y = x 2 is positive at its rightmost points and leftmost points. 49. GEOMETRY The measures of two angles of a triangle are x and 4x. Which of these expressions represents the measure of the third angle? F x + 4x G 180 x 4x H 180 x + 4x J x 4x G esolutions Manual - Powered by Cognero Page 9
10 50. GRIDDED RESPONSE Find the value of x that makes 6 true. 52. Graph each function. Identify the domain and range. 51. ACT/SAT Which could be the inequality for the graph? D = {all real numbers} A 53. B C D E A D = {all real numbers} R = {all integers} esolutions Manual - Powered by Cognero Page 10
11 Solve each inequality. 57. D = {all real numbers} ATTENDANCE The table shows the annual attendance to West High School s Summer Celebration. a. Find a regression equation for the data. b. Determine the correlation coefficient. c. Predict how many people will attend the Summer Celebration in CARS Loren is buying her first car. She is considering 4 different models and 5 different colors. How many different cars could she buy? 20 Determine if each relation is a function. a. y = 7.83x b. r = c. about 118 people 60. no esolutions Manual - Powered by Cognero Page 11
12 61. yes 62. yes Evaluate each expression if x = 4 and y = x 8y y + 3x x + 10y esolutions Manual - Powered by Cognero Page 12
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