Parent Functions and Transformations Worksheet
Connect parent functions with transformed graphs. Includes a worked example, printable practice, and an answer key with explanations.
The answer key follows the practice below. In the editor, remove the final answer-key section before sharing a student copy.
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Parent Functions and Transformations
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Learning goal and worked example
Connect parent functions with transformed graphs.
For g(x) = −|x−1|+2, the vertex is (1,2), the graph opens downward, and points (0,1) and (2,1) confirm symmetry.
Prerequisites: quadratic, absolute-value, cubic, and square-root parent functions. State the order when shifts and scales interact.
Read each question carefully and follow the instructions to determine the parent function, describe the transformations, or sketch the graphs.
1. Which of the following is the parent function for f(x) = (x - 3)² + 1?
f(x) = x
f(x) = x²
f(x) = x³
f(x) = |x|
2. Which transformation is represented by g(x) = -f(x)?
Vertical stretch
Horizontal shift
Reflection across x-axis
Reflection across y-axis
1. A transformation that shifts a graph left or right is called a shift.
2. When a function is multiplied by a constant 'a' such that |a| > 1, it results in a vertical .
3. The parent function for a cubic function is f(x) = .
1. Describe the transformations applied to the parent function f(x) = |x| to obtain g(x) = -2|x + 4| - 5.
2. Write the equation of the function that results from shifting the parent function f(x) = √x up 3 units and reflecting it across the y-axis.
1. Sketch the graph of the parent function f(x) = x² and the transformed function g(x) = -(x - 2)² + 3 on the same coordinate plane.
2. Sketch the graph of the parent function f(x) = |x| and the transformed function h(x) = ½|x| - 1 on the same coordinate plane.
1. A vertical compression occurs when a function is multiplied by a constant 'a' such that 0 < |a| < 1.
True
False
2. The order of transformations (reflections, stretches/compressions, and translations) does not affect the final graph.
True
False
Answer key and worked solutions
Multiple choice: 1 b (x²); 2 c (reflection across x-axis).
Fill in the blanks: 1 horizontal; 2 stretch; 3 x³.
Short answer 1: left 4, vertical stretch by 2, reflection across x-axis, then down 5; vertex (−4,−5).
Short answer 2: g(x)=√(−x)+3, with domain x≤0 and range y≥3.
Graphing 1: Parent vertex (0,0), points (±1,1),(±2,4). Transformed vertex (2,3), points (1,2),(3,2),(0,−1),(4,−1), opening downward.
Graphing 2: Parent vertex (0,0), points (±2,2). Transformed vertex (0,−1), points (±2,0),(±4,1); both are V-shaped and open upward.
True/false: 1 True. 2 False: shifting x² up 1 then stretching vertically by 2 gives 2x²+2; reversing the order gives 2x²+1.
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