Stretching or Compressing a Graph

In this lesson, we will learn about graphing function transformations known as function dilation or simply stretching or shrinking a graph. We will explore what happens when a function g(x) is defined by multiplying a related function f(x) by some positive real number a. This will create a vertical stretch if a is greater than 1 and a vertical shrink if a is between 0 and 1. Additionally, we will explore horizontal stretches and compressions. These occur when a function such as g(x) is defined by plugging in ax for x in the function f(x), so essentially this becomes g(x) = f(ax). Here if a is larger than 1, we have a horizontal compression and if a is between 0 and 1, we will have a horizontal stretch.