Transformation of Graphs Worksheet
Grade 9 math worksheet on understanding and applying transformations to various functions including translations, reflections, and dilations.
Includes
Standards
Topics
Transformation of Graphs
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Read each question carefully and follow the instructions. Show all your work where applicable.
1. If the graph of y = f(x) is shifted 3 units to the right, which of the following represents the new equation?
y = f(x) + 3
y = f(x) - 3
y = f(x + 3)
y = f(x - 3)
2. Reflecting the graph of y = x² across the x-axis results in which equation?
y = (-x)²
y = -x²
y = x² + 1
y = x² - 1
3. A vertical stretch by a factor of 2 applied to y = f(x) yields the equation y = .
4. When the graph of y = f(x) is translated 5 units down, the new equation is y = .
5. A reflection across the y-axis changes f(x) to f( ).
6. Describe the sequence of transformations that transforms the graph of y = x² to y = -2(x + 1)² + 3.
7. The graph of y = |x - 4| is the graph of y = |x| shifted 4 units to the left.
True
False
8. A horizontal compression by a factor of 1/2 means replacing x with 2x in the function's equation.
True
False
9. The graph of y = x³ is shown below. On the same coordinate plane, sketch the graph of y = -(x - 2)³ + 1.