Horizontal Transformations

Horizontal Transformations can be tricky. But by approaching the problem in the way explained below, we make recognizing horizontal transformations easier.


Suppose we have a function , and we want to plot the graph of . Shifting this graph may seem difficult, but by following these steps, we can clearly see the transformed graph. Step 1: Pick an x-value. Step 2: Shift the x-value to x+h. Step 3: Find f(x+h). Step 4: Plot f(x+h) at the original x-value. The ordered pair will be (x,f(x+h)). Step 5: Repeat for other values of x until you see a trend.

Shift the slider up to see each step of the transformation.