AP Precalc 1.12B Notes 1.12B Dilations of Functions Write your questions and thoughts here! Multiplicative Transformations Dilations = Graphically Example #1 Vertical Dilations Given the graph 𝑓. Let 𝑔 𝑥 Given the graph 𝑓. 2𝑓 𝑥 , graph 𝑔 𝑥 Let 𝑔 𝑥 𝑓 𝑥 , graph 𝑔 𝑥 Example #2 Horizontal Dilations Given the graph 𝑓. Let 𝑔 𝑥 Given the graph 𝑓. 𝑓 2𝑥 , graph 𝑔 𝑥 . Let 𝑔 𝑥 𝑓 𝑥 , graph 𝑔 𝑥 . Given the graph 𝑓. Let 𝑔 𝑥 𝑓 𝑥 , graph 𝑔 𝑥 . Example #3 Given the graph 𝑓. Let 𝑔 𝑥 3𝑓 𝑥 2 , graph 𝑔 𝑥 . Given the graph 𝑓. Let 𝑔 𝑥 𝑓 2 𝑥 3 1 , graph 𝑔 𝑥 . Write your questions and thoughts here! Algebraically Example 4: Given 𝑓 𝑥 Let 𝑔 𝑥 2𝑓 𝑥 𝑥 3𝑥 Given 𝑓 𝑥 2 4 , find 𝑔 𝑥 . Let 𝑔 𝑥 𝑓 𝑥 6𝑥 3 2 , find 𝑔 𝑥 . Numerically Example #5 Given the table of values for 𝑓. Let 𝑔 𝑥 𝒙 2 1 0 1 2 𝒇 𝒙 21 12 18 14 10 5𝑓 𝑥 1 , find 𝑔 Given the table of values for 𝑓. 𝒙 0 1 2 3 4 1 . Let 𝑔 𝑥 𝑓 3 𝑥 𝒇 𝒙 20 12 0 8 14 1 2 , find 𝑔 2 . Domain and Range Example #6 Given the graph for 𝑓 has a domain of Find the domain and range of 𝑔 𝑥 . 2,5 and range of 4, 9 . Let 𝑔 𝑥 3𝑓 𝑥 2. 1.12B Dilations of Functions 1.12B Practice AP Precalculus GRAPHICAL TRANSFORMATION. Use the graph of 𝒇 to graph 𝒈 𝒙 . 1. 𝑔 𝑥 3𝑓 𝑥 4. 𝑔 𝑥 𝑓 𝑥 5 2. 𝑔 𝑥 𝑓 𝑥 5. 𝑔 𝑥 𝑓 𝑥 4 3. 𝑔 𝑥 𝑓 𝑥 2 6. 𝑔 𝑥 𝑓 2 𝑥 1 ALGEBRAIC TRANSFORMATION. Express the 𝒈 𝒙 in terms of 𝒙. 7. 𝑓 𝑥 𝑔 𝑥 9. 𝑓 𝑥 𝑔 𝑥 4𝑥 3𝑓 𝑥 4𝑥 8. 𝑓 𝑥 3 5 , find 𝑔 𝑥 . 5 2𝑓 𝑥 𝑔 𝑥 10. 𝑓 𝑥 1 5 , find 𝑔 𝑥 . 𝑔 𝑥 2𝑥 6 𝑓 𝑥 2𝑥 𝑓 2𝑥 2 3𝑥 1 , find 𝑔 𝑥 . 1 3 , find 𝑔 𝑥 . NUMERIC TRANSFORMATION. Use the table of values to answer the following. 11. Given the table of values for 𝑓. 𝒙 9 3 2 6 8 Let 𝑔 𝑥 𝑓 3𝑥 12. Given the table of values for 𝑓. 𝒇 𝒙 2 8 15 2 13 1 , find 𝑔 2 . 𝒙 0 1 2 3 4 Let 𝑔 𝑥 2𝑓 𝑥 13. Given the table of values for 𝑓. 𝒇 𝒙 0 2 4 8 16 2 𝒙 8 2 0 2 8 3 , find 𝑔 1 . Let 𝑔 𝑥 𝒇 𝒙 32 6 8 21 14 4𝑓 𝑥 , find 𝑔 2 . DOMAIN AND RANGE TRANSFORMATION. Find the domain and range of the transformed function. 14. Given the graph for 𝑓 has a domain of 6,8 and range of 4, 8 . Let 𝑔 𝑥 15. Given the graph for 𝑓 has a domain of 0,5 and range of 10,4 . 3𝑓 2𝑥 . Find the domain and range of 𝑔 𝑥 . Let 𝑔 𝑥 2𝑓 𝑥 3 16. Given the graph for 𝑓 has a domain of 2,4 and range of 6, 8 . 4. Let 𝑔 𝑥 Find the domain and range of 𝑔 𝑥 . 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. 𝑥 5. Find the domain and range of 𝑔 𝑥 . Use the graph 𝒇 to answer the following. 17. 𝑓 Find the y-intercept of 𝑔 𝑥 .