Function Transformation Calculator

Pick one of eleven parent functions and the four numbers in g(x) = a f(b(x - h)) + k, and this writes out what the transformation does. It returns the transformed equation, the stretches, reflections and shifts in the order they act on a point, where each of the parent's key points ends up, and the domain, range, asymptotes, vertex and intercepts of the result. A second action lays the parent and the transformed function side by side in a table of values. The horizontal numbers are the ones that catch people out, so b is reported as a factor of 1/|b| and the page says plainly that a f(bx - c) + k shifts by c/b rather than by c.

Calculator Type

Pick a parent function and the four numbers in g(x) = a f(b(x - h)) + k. You get the equation, the transformations in the order they happen, where the key points land, and the domain, range, asymptotes and intercepts of the result.

Parent Function f(x)

a, the vertical stretch

Multiplies the output. Negative flips the graph over the x-axis.

b, the horizontal stretch

Multiplies the input, so it does the opposite of what it looks like: b = 3 squeezes the graph to a third of its width. Negative flips it over the y-axis.

h, the horizontal shift

Positive moves the graph right. In the written form it appears as x - h, which is why the sign looks backwards.

k, the vertical shift

Positive moves the graph up.

Widget

The parent and the transformed function side by side across a range of x.