Parent Functions and Transformations Worksheet
Explore parent functions and their transformations including translations, reflections, and dilations with this Grade 9 math worksheet.
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Parent Functions and Transformations
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Which of the following is the parent function of a quadratic equation?
f(x) = x
f(x) = |x|
f(x) = x²
f(x) = √x
2. A vertical shift of a function moves the graph or .
3. The graph of f(x) = -x² is a of the parent function f(x) = x² across the x-axis.
4. Describe the transformation applied to the parent function f(x) = x to get the function g(x) = x - 3.
5. A horizontal compression of a function occurs when a > 1 in the transformation f(ax).
True
False
6. Graph the parent function f(x) = x³ and the transformed function g(x) = (x + 2)³ - 1 on the coordinate plane below.
Match each transformation with its description.
7. f(x) + c
a. Horizontal shift left
8. f(x - c)
b. Vertical shift up
9. -f(x)
c. Reflection across the x-axis
10. f(-x)
d. Reflection across the y-axis