Practice Function Transformation in Math

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

Quick Recap

A function transformation shifts, stretches, compresses, or reflects the graph of a parent function by modifying its formula in a systematic way.

Moving or reshaping a graph without changing its basic shape.

Example 1

easy
Describe all transformations applied to f(x) = x^2 to obtain g(x) = 2(x-3)^2 + 1.

Example 2

medium
Starting from f(x) = \sqrt{x}, apply the transformation g(x) = -\sqrt{2x+4} step by step and identify the key point transformations.

Example 3

easy
The graph of y = f(x) passes through (1, 4). Where does the transformed graph y = f(x+2) - 3 pass through?

Example 4

hard
Write the equation of the function obtained by reflecting f(x)=\log_2(x) over the y-axis, compressing horizontally by a factor of 3, and shifting up 5.