. Given the function y = - (x - 1)2 + 1. What is the parent function? Graph it. List, in order, the steps of transformation that the primary functions underwent to become the function given before. Graph the given function, using

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.5: Transformation Of Functions
Problem 58SE: For the following exercises, describe how the graph of each function is a transformation of the...
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1. Given the function y = - (x - 1)2 + 1.

What is the parent function? Graph it.

List, in order, the steps of transformation that the primary functions underwent to become the function given before.

Graph the given function, using the steps list in b.

Expert Solution
Step 1: Given function

y equals negative open parentheses x minus 1 close parentheses squared plus 1

Remember the following transformations:

straight f open parentheses straight x minus straight a close parentheses space Shift space straight f open parentheses straight x close parentheses space to space the space right space straight a space units
minus straight f open parentheses straight x close parentheses space Reflect space straight f open parentheses straight x close parentheses space along space straight x space axis
straight f left parenthesis straight x right parenthesis plus straight a space shifts space straight f left parenthesis straight x right parenthesis space upwards space straight a space units

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