Function Transformations

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

A vertical shift moves the graph of the function up or down without changing its shape.

Adding a constant k to a function shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

The expression f(x - h) represents a horizontal shift of the graph to the right by h units.

The expression f(x + h) represents a horizontal shift of the graph to the left by h units.

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

A negative sign in front of a function reflects the graph across the x-axis.

The parent function of a quadratic function is f(x) = x².

The transformation f(x) = f(-x) reflects the graph across the y-axis.