AP Precalculus 1.12B Dilations of Functions PDF
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This document contains notes and practice problems for AP Precalculus, specifically covering dilations of functions. These include examples of both graphical and algebraic techniques in solving problems about the topic of transformations. Problems range from identifying transformations from graphs to calculating domains and ranges.
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AP Precalc 1.12B Dilations of Functions 1.12B Notes Write your questions and thoughts here! Multiplicative Transformations Dilations =...
AP Precalc 1.12B Dilations of Functions 1.12B Notes Write your questions and thoughts here! Multiplicative Transformations Dilations = Graphically Example #1 Vertical Dilations Given the graph 𝑓. Given the graph 𝑓. Let 𝑔 𝑥 2𝑓 𝑥 , graph 𝑔 𝑥 Let 𝑔 𝑥 𝑓 𝑥 , graph 𝑔 𝑥 Example #2 Horizontal Dilations Given the graph 𝑓. Given the graph 𝑓. Given the graph 𝑓. Let 𝑔 𝑥 𝑓 2𝑥 , graph 𝑔 𝑥. Let 𝑔 𝑥 𝑓 𝑥 , graph 𝑔 𝑥. Let 𝑔 𝑥 𝑓 𝑥 , graph 𝑔 𝑥. Example #3 Given the graph 𝑓. Given the graph 𝑓. Let 𝑔 𝑥 3𝑓 𝑥 2 , graph 𝑔 𝑥. Let 𝑔 𝑥 𝑓 2 𝑥 3 1 , graph 𝑔 𝑥. © The Algebros from FlippedMath.com Write your questions Algebraically and thoughts here! Example 4: Given 𝑓 𝑥 𝑥 3𝑥 2 Given 𝑓 𝑥 6𝑥 3 Let 𝑔 𝑥 2𝑓 𝑥 4 , find 𝑔 𝑥. Let 𝑔 𝑥 𝑓 𝑥 2 , find 𝑔 𝑥. Numerically Example #5 Given the table of values for 𝑓. Given the table of values for 𝑓. 𝒙 𝒇 𝒙 𝒙 𝒇 𝒙 2 21 0 20 1 12 1 12 0 18 2 0 1 14 3 8 2 10 4 14 Let 𝑔 𝑥 5𝑓 𝑥 1 , find 𝑔 1. Let 𝑔 𝑥 𝑓 3 𝑥 1 2 , find 𝑔 2. Domain and Range Example #6 Given the graph for 𝑓 has a domain of 2,5 and range of 4, 9. Let 𝑔 𝑥 3𝑓 𝑥 2. Find the domain and range of 𝑔 𝑥. © The Algebros from FlippedMath.com 1.12B Dilations of Functions AP Precalculus 1.12B Practice GRAPHICAL TRANSFORMATION. Use the graph of 𝒇 to graph 𝒈 𝒙. 1. 𝑔 𝑥 3𝑓 𝑥 5 2. 𝑔 𝑥 𝑓 𝑥 3. 𝑔 𝑥 𝑓 𝑥 2 4. 𝑔 𝑥 𝑓 𝑥 5. 𝑔 𝑥 𝑓 𝑥 4 6. 𝑔 𝑥 𝑓 2 𝑥 1 ALGEBRAIC TRANSFORMATION. Express the 𝒈 𝒙 in terms of 𝒙. 7. 𝑓 𝑥 4𝑥 3 8. 𝑓 𝑥 2𝑥 6 𝑔 𝑥 3𝑓 𝑥 5 , find 𝑔 𝑥. 𝑔 𝑥 𝑓 𝑥 2 1 , find 𝑔 𝑥. 9. 𝑓 𝑥 4𝑥 5 10. 𝑓 𝑥 2𝑥 3𝑥 1 𝑔 𝑥 2𝑓 𝑥 1 5 , find 𝑔 𝑥. 𝑔 𝑥 𝑓 2𝑥 3 , find 𝑔 𝑥. © The Algebros from FlippedMath.com NUMERIC TRANSFORMATION. Use the table of values to answer the following. 11. Given the table of values for 𝑓. 12. Given the table of values for 𝑓. 13. Given the table of values for 𝑓. 𝒙 𝒇 𝒙 𝒙 𝒇 𝒙 𝒙 𝒇 𝒙 9 2 0 0 8 32 3 8 1 2 2 6 2 15 2 4 0 8 6 2 3 8 2 21 8 13 4 16 8 14 Let 𝑔 𝑥 𝑓 3𝑥 1 , find 𝑔 2. Let 𝑔 𝑥 2𝑓 𝑥 2 3 , find 𝑔 1. Let 𝑔 𝑥 4𝑓 𝑥 , find 𝑔 2. DOMAIN AND RANGE TRANSFORMATION. Find the domain and range of the transformed function. 14. 15. 16. Given the graph for 𝑓 has a domain Given the graph for 𝑓 has a domain of Given the graph for 𝑓 has a domain of 6,8 and range of 4, 8. 0,5 and range of 10,4. of 2,4 and range of 6, 8. Let 𝑔 𝑥 3𝑓 2𝑥. Let 𝑔 𝑥 2𝑓 𝑥 3 4. Let 𝑔 𝑥 𝑓 𝑥 5. Find the domain and range of 𝑔 𝑥. Find the domain and range of 𝑔 𝑥. Find the domain and range of 𝑔 𝑥. Use the graph 𝒇 to answer the following. 17. Let the 𝑔 𝑥 2𝑓 𝑥 3 1 a. Graph the 𝑔 𝑥. b. State the domain of 𝑔 𝑥. c. State the range of 𝑔 𝑥. d. Find 𝑔 2. e. Find the zeroes of 𝑔 𝑥. f. Find the y-intercept of 𝑔 𝑥. © The Algebros from FlippedMath.com 1.12B Dilations of Functions 1.12B Test Prep Multiple Choice 18. The graph of 𝑦 𝑓 𝑥 is shown for 3 𝑥 4. Which of the following is the transformed graph for 𝑦 𝑓 2𝑥 ? (A) (B) (C) (D) 19. The table gives values for a polynomial function 𝑓 at selected values of 𝑥. 𝒙 2 0 2 4 8 16 𝒇 𝒙 38 12 -24 -32 -12 -48 In the xy-plane, the graph of 𝑔 is constructed by applying three transformations to the graph of 𝑓 in this order: a horizontal dilation of , a vertical dilation of 4 and vertical translation by 6 units. What is the value of 𝑔 4 ? (A) 3 (B) 42 (C) 90 (D) 0 20. The function 𝑔 is defined by 𝑓 such that 𝑔 𝑥 3𝑓 2𝑥 𝑏. If 𝑓 2 𝑎, 𝑓 4 8, 𝑔 1 7 and 𝑔 2 19 what is the value of a ? (A) 6 (B) 4 (C) 2 (D) 2 © The Algebros from FlippedMath.com
