Function Transformations

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

A parent function is the simplest form of a function type, from which other functions in the same family are derived.

A vertical stretch increases the distance between points on the graph and the x-axis, making the graph taller.

A vertical compression decreases the distance between points on the graph and the x-axis, making the graph shorter.

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

Subtracting a constant h from the input translates the graph horizontally to the right by h units.

Adding a constant h to the input translates the graph horizontally to the left by h units.

A reflection over the x-axis flips the graph of the function upside down.

A reflection over the y-axis flips the graph of the function horizontally.

A vertical stretch by a factor of a is represented as f(x) = a * f(x), where a > 1.