**When ***y = a * f(x)*, multiply the *y* values of *f(x)* by *a*. Leave the *x* values alone. This is a vertical stretch (if *|a| > 1*) or shrink (if *|a| < 1*). Example: **1. Problem: Given is a graph of ***y = f(x)*. Sketch *y = 2f(x)*. The figure below is the graph of *f(x)*. **Solution:** Multiply values of

*y* by

*2* and keep the same

*x* values. Then redraw the graph. The figure below is the graph of the solution.

**When ***y = f(b * x)*, divide the *x* values of *f(x)* by *b*. Leave the *y* values alone. This is a horizontal stretch (if *|b| < 1*) or shrink (if *|b| > 1*). Example: **2. Problem: Given is a graph of ***y = f(x)*. Sketch *y = f(.5x)*. The figure below is the graph of *y = f(x)*. **Solution:** Divide each

*x* value by

*.5* (same as multiplying by

*2*). Keep same

*y* values, and redraw the graph. The figure below is a graph of the solution.