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, most basic version of a function family — the unshifted, unstretched, unreflected template. All other functions in the family are transformations of this parent. Memorizing parent function shapes allows rapid graphing of transformed versions.

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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