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
easyDescribe all transformations applied to f(x) = x^2 to obtain g(x) = 2(x-3)^2 + 1.
Example 2
mediumStarting from f(x) = \sqrt{x}, apply the transformation g(x) = -\sqrt{2x+4} step by step and identify the key point transformations.
Example 3
easyThe graph of y = f(x) passes through (1, 4). Where does the transformed graph y = f(x+2) - 3 pass through?
Example 4
hardWrite 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.