Parent Function Transformations

A parent function is the simplest form of a function in a family of functions. It serves as a reference point for transformations.

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

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

The transformation y = f(x) + k shifts the graph of the function f(x) vertically by k units. If k is positive, it shifts up; if negative, it shifts down.

The transformation y = f(x + h) shifts the graph of the function f(x) horizontally by h units. If h is positive, it shifts left; if negative, it shifts right.

The transformation y = af(x) vertically stretches or compresses the graph of the function f(x). If |a| > 1, it stretches; if 0 < |a| < 1, it compresses.

The transformation y = f(bx) horizontally stretches or compresses the graph of the function f(x). If |b| > 1, it compresses; if 0 < |b| < 1, it stretches.

The point (4,3) moves to (-4,1) on the graph of y=-f(-x)+4.

The point (-1,4) moves to (-2,4) on the graph of y=2f(x+1)-4.

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