AP Precalculus 1.12A Translations of Functions PDF

AP Precalc 1.12A Translations of Functions 1.12A Notes Write your questions and thoughts here! Additive Transformations Translations = G...

AP Precalc 1.12A Translations of Functions 1.12A Notes Write your questions and thoughts here! Additive Transformations Translations = Graphically Example #1 Given the graph 𝑓. Given the graph 𝑓. Let 𝑔(𝑥) = 𝑓(𝑥) + 4 , graph 𝑔(𝑥) Let 𝑔(𝑥) = 𝑓(𝑥 + 4) , graph 𝑔(𝑥) Example #2 Given the graph 𝑓. Given the graph 𝑓. Let 𝑔(𝑥) = 𝑓(𝑥) − 4 , graph 𝑔(𝑥). Let 𝑔(𝑥) = 𝑓(𝑥 − 4) , graph 𝑔(𝑥). Example #3 Vertical Reflection Given the graph 𝑓. Given the graph 𝑓. Let 𝑔(𝑥) = −𝑓(𝑥) , graph 𝑔(𝑥). Let 𝑔(𝑥) = −𝑓(𝑥 − 2) + 5 , graph 𝑔(𝑥). © The Algebros from FlippedMath.com Write your questions and thoughts here! Algebraically Example 4: Given 𝑓 (𝑥 ) = 𝑥 2 − 3𝑥 + 2 Given 𝑓 (𝑥 ) = 𝑥 2 − 3𝑥 + 2 Let 𝑔(𝑥) = 𝑓(𝑥) + 4 , find 𝑔(𝑥). Let 𝑔(𝑥) = 𝑓(𝑥 + 4) , 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) = 𝑓(𝑥) + 2 , find 𝑔(2). Let 𝑔(𝑥) = 𝑓(𝑥 − 2) + 1 , find 𝑔(4). Domain and Range Example #6 Given the graph for 𝑓 has a domain of [−4,3] and range of (3, 9). Let 𝑔(𝑥) = −𝑓(𝑥 + 5) + 2. Find the domain and range of 𝑔(𝑥). © The Algebros from FlippedMath.com 1.12A Translations of Functions AP Precalculus 1.12A Practice GRAPHICAL TRANSFORMATION. Use the graph of 𝒇 to graph 𝒈(𝒙). 1. 𝑔(𝑥) = 𝑓(𝑥 − 2) + 4 2. 𝑔(𝑥) = −𝑓(𝑥 + 3) 3. 𝑔(𝑥) = −𝑓(𝑥) + 5 4. 𝑔(𝑥) = 𝑓(𝑥 − 5) − 3 5. 𝑔(𝑥) = 𝑓(𝑥) − 4 6. 𝑔(𝑥) = −𝑓(𝑥 − 3) + 1 ALGEBRAIC TRANSFORMATION. Express the 𝒈(𝒙) in terms of 𝒙. 7. 𝑓(𝑥) = 4𝑥 + 3 8. 𝑓(𝑥) = 2𝑥 − 5 𝑔(𝑥) = 𝑓(𝑥) + 5 , find 𝑔(𝑥). 𝑔(𝑥) = 𝑓(𝑥 + 3) + 4 , find 𝑔(𝑥). 9. 𝑓(𝑥) = 𝑥 3 + 2𝑥 2 10. 𝑓(𝑥) = 2𝑥 2 − 3𝑥 + 1 𝑔(𝑥) = −𝑓(𝑥) + 5 , find 𝑔(𝑥). 𝑔(𝑥) = 𝑓(𝑥 − 2) + 5 , 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) −6 2 0 0 −4 −32 −3 8 1 2 −2 6 2 15 2 4 0 −8 5 −2 3 8 2 21 8 −13 4 16 4 14 Let 𝑔(𝑥) = 𝑓(𝑥) + 2 , find 𝑔(5). Let 𝑔(𝑥) = 𝑓(𝑥 + 2) − 3 , find 𝑔(1). Let 𝑔(𝑥) = −𝑓(𝑥 − 2) , find 𝑔(4). 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 (−5,3] and range of [−4, 8]. (0,5) and range of [−10,4]. of [−2,4] and range of (−1, 8). Let 𝑔(𝑥) = 𝑓(𝑥 + 5). Let 𝑔(𝑥) = 𝑓(𝑥 − 2) + 4. Let 𝑔(𝑥) = −𝑓(𝑥 + 3) + 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) = −𝑓(𝑥 + 3) + 2 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 1.12A Translations of Functions 1.12A 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(𝑥 + 2) − 1 ? (A) (B) (C) (D) 19. The functions 𝑓 and 𝑔 are defined for all real numbers such that 𝑔(𝑥) = −𝑓(𝑥) + 5. Which of the following sequences of transformations maps the graph of 𝑓 to the graph of 𝑔 in the same 𝑥𝑦-plane? (A) A horizontal translation of the graph of 𝑓 by 5 units, followed by a vertical reflection of the graph of 𝑓. (B) A vertical translation of the graph of 𝑓 by 5 units, followed by a vertical reflection of the graph of 𝑓. (C) A vertical reflection of the graph of 𝑓, followed by a horizontal translation of the graph of 𝑓 by 5 units. (D) A vertical reflection of the graph of 𝑓, followed by a vertical translation of the graph of 𝑓 by 5 units. 20. The function 𝑓 is given by 𝑓(𝑥) = −𝑥 2 + 3𝑥 + 2. The graph of which of the following functions is the image of the graph of 𝑓 after a vertical translation of the graph of 𝑓 by 4 units ? (A) 𝑚(𝑥) = −(𝑥 + 4)2 + 3(𝑥 + 4) + 2, because this is an additive transformation of 𝑓 that results from adding to each input value of 𝑥. (B) 𝑛(𝑥) = −(𝑥 − 4)2 + 3(𝑥 − 4) + 2, because this is an additive transformation of 𝑓 that results from adding to each input value of 𝑥. (C) 𝑝(𝑥) = −𝑥 2 + 3𝑥 + 6, because this is an additive transformation of 𝑓 that results from adding to the 𝑓(𝑥). (D) 𝑞(𝑥) = −𝑥 2 + 3𝑥 − 2, because this is an additive transformation of 𝑓 that results from adding to the 𝑓(𝑥). © The Algebros from FlippedMath.com