# Function Transformations

The applet below allows you to look at the effects on graphs of functions when stretched, compressed, or shifted vertically or horizontally.
If f(x) is a function then:
f(x + h) shifts f to the left by h units (or to the right if h is negative)
f(bx + h) is equivalent to f(b(x + h/b)), which means that first the function is compressed by a factor of b (when b > 1) or stretched when 0 < b < 1. When b is negative, the function flips horizontally across a vertical line.
a f(x) stretches f vertically when a is >1. When 0 < a < 1, the function is compressed vertically. When a is negative, the function flips across the y-axis
f(x) + k shifts f k units up or down.
----------------
Using the applet:

- The function slider allows you to examine different parent functions.
- The phases slider allows you to break down the transformation a f(bx + h) + k to look at the effect of each on the equation and on the coordinates of an image point.
- The Point Calculation will take you back and forth between looking at the equation of the transformed function and looking at the calculation of the coordinates of the image point.
- The Reset button sets the values of a, b, h, and k back to their default settings.

## New Resources

## Discover Resources

Download our apps here: