Function Transformations

A function transformation refers to the changes made to the graph of a function, including shifts, stretches, compressions, and reflections.

The parent function of an absolute value function is $$f(x) = |x|$$ .

A vertical stretch multiplies the output values of the function by a factor greater than 1, making the graph taller.

The transformed function is $$f(x) = |x - 3|$$ .

Reflecting a function across the x-axis changes the sign of the output values, resulting in a vertical flip of the graph.

The transformed function is $$f(x) = |2x|$$ .

The transformed function is $$f(x) = |x| - 4$$ .

This represents a vertical shrink by a factor of 1/2.

The transformed function is $$f(x) = |x + 2|$$ .

The transformed function is $$f(x) = 3|x|$$ .