Module 1: Function Transformations

 

Lesson 3 Summary

 

When you multiply all of the x-coordinates or y-coordinates of a function by a constant, the change in shape is called a stretch. When you're stretching about the x-axis or the y-axis, it is useful to think of a function in terms of the equation y = af(bx). When using an equation of this form, a corresponds to a vertical stretch about the x-axis by a factor of a. And b corresponds to a horizontal stretch about the y-axis by a factor of .

 

This diagram shows two functions being stretched. The first diagram shows a vertical stretch about the x-axis, and the figure appears taller if a is greater than 1 and shorter if 0 is less than a is less than 1. The second diagram shows a horizontal stretch about the y-axis and the figure appears wider if 0 is less than b is less than 1 and narrower if b is greater than 1.

 

Now is a good time to update your summary table for the stretches you learned in this lesson. In Lesson 4 you will begin to combine the transformations learned so far.