Practice Parent Functions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A parent function is the simplest base graph in a function family before transformations.

It is the original template shape you move, stretch, or reflect.

Example 1

easy
Identify the parent function of f(x) = 3(x - 2)^2 + 5 and describe the transformations.

Example 2

medium
Match each equation to its parent function: (a) y = -\sqrt{x+3}, (b) y = \frac{2}{x-1}, (c) y = |x| - 4, (d) y = 2^{x+1} - 3.

Example 3

medium
Sketch the key features (domain, range, intercepts, asymptotes) of the parent function y = \frac{1}{x}.

Example 4

hard
Write a single equation using transformations of the parent function y = \sqrt{x} that has domain (-\infty, 4], range [-2, \infty), and passes through the point (0, 0).
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