Parent Functions and Transformations
Explore parent functions and their transformations including translation, reflection, stretching, and compression.
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Parent Functions and Transformations
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. Which transformation shifts the graph of a function horizontally?
f(x) + c
f(x + c)
c * f(x)
-f(x)
2. The graph of y = x² is transformed to y = (x - 3)² + 1. Describe the transformations.
Shift left 3, up 1
Shift right 3, up 1
Shift left 3, down 1
Shift right 3, down 1
3. A vertical stretch by a factor of 2 applied to f(x) results in the function g(x) = .
4. Reflecting the graph of f(x) across the x-axis results in the function g(x) = .
5. Describe the transformations applied to the parent function f(x) = |x| to obtain the graph of g(x) = -2|x + 4| - 5.
6. The function g(x) = f(-x) represents a reflection of f(x) across the y-axis.
True
False
7. Graph the parent function y = x³ and the transformed function y = (x + 2)³ - 1 on the coordinate plane below.