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Name______________________________________________________________________Date_____________Period_______A#_B-β14_ Translations and Mapping Notation 1. Using your graphing calculator, graph π¦! = π₯ ! . 2. Graph π¦! = π₯ ! . Now graph π¦! = (π₯ + 4)! . What is ! the effect of replacing π₯ with (π₯ + 4)? Sketch the Now graph π¦! = (π₯ β 3) . What is the effect of replacing π₯ with (π₯ β 3)? Sketch the graphs with graphs with arrows to show the translation. arrows to show the translation. 3. Repeat 1 and 2 above, but use the square root function. That is, graph π¦! = π₯ and compare it to π¦! = π₯ β 3. Then graph π¦! = π₯ and compare it to π¦! = π₯ + 4. Write a generalization of what happens to the graph of π¦ = π(π₯) when π₯ is replaced with (π₯ β β) to get π¦ = π(π₯ β β). (Assume that β > 0.) A sketch may be helpful. ! 5. Graph π¦! = π₯ . Now graph π¦! = π₯ β 4. This is 4. Using your graphing calculator, graph π¦! = !. equivalent to π¦! + 4 = π₯ . What is the effect of ! Now graph π¦! = ! + 3. This is equivalent to replacing π¦ with (π¦ + 4)? Sketch the graphs with ! arrows to show the translation. π¦! β 3 = !. What is the effect of replacing y with (y β 3)? Sketch the graphs with arrows to show the translation. 6. Write a generalization of what happens to the graph of π¦ = π(π₯) when π¦ is replaced with (π¦ β π) to get π¦ β π = π(π₯). (Assume that π > 0.) ! 8. Write a generalization of what happens to the 7. Using your graphing calculator, graph π¦! = ! ! . graph of π¦ = π(π₯) when π₯ is replaced with ! Now graph π¦! = (!!!)! + 2. This is equivalent to (π₯ β β) and π¦ is replaced with (π¦ β π) to get ! π¦ β π = π(π₯ β β). (Assume that β > 0 and π > 0.) π¦! β 2 = (!!!)! . What is the effect of replacing π₯ with (π₯ β 5) and π¦ with (π¦ β 2)? Sketch the graphs with arrows to show the translation. Adapted from the work of Nils Ahbel. www.ahbel.com Your answers to #1 and #4 should have been something like, βThe graph moved 3 units to the rightβ and βThe graph moved 3 units upβ. Mapping notation is convenient to communicate translations. We sayβ¦ In mapping notation this looks likeβ¦ βThe graph is translated 3 units to the right.β π: (π₯, π¦) β (π₯ + 3, π¦) βThe graph is translated 3 units up.β π: (π₯, π¦) β (π₯, π¦ + 3) π : (π₯, π¦) β (π₯ + 3, π¦) βThe transformation such that any point (π₯, π¦) maps to (π₯ + 3, π¦).β 9. Write a rule in mapping notation for the transformation that maps π(π₯) = πππ(π₯) to π(π₯) = πππ(π₯ + 4). Note: you do not need to know anything about the graph of π(π₯) = πππ(π₯) in order to do this problem. 10. Write a rule in mapping notation for the transformation that maps π π₯ = 2! to π π₯ = 2!!! . Note: you do not need to know anything about the graph of π π₯ = 2! in order to do this problem. 11. The graph of the function below is the graph of π(π₯) = |π₯| after the transformation 12. The graph of the function below is the graph of π(π₯) = π₯ ! after the transformation π: (π₯, π¦) β (π₯ β 3, π¦ + 1). π: (π₯, π¦) β (π₯ + 1, π¦ + 2). What is the equation of the graph below? Note the graph passes through (1,5). Test to see if your equation includes (1,5). If not, you made a mistake. What is the equation of the graph below? Test your answer using the method in #11. Adapted from the work of Nils Ahbel. www.ahbel.com