Parent Functions and Transformations Worksheet

Parent Functions and Transformations

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?

2. Which transformation is represented by g(x) = -f(x)?

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.

2. The order of transformations (reflections, stretches/compressions, and translations) does not affect the final graph.