In Try This 2 you may have noticed that the function y = af(bx) is the function y = f(x) stretched about the y-axis by a factor of 
and stretched about the x-axis by a factor of a.
In Try This 2 you may have noticed that the function y = af(bx) is the function y = f(x) stretched about the y-axis by a factor of and stretched about the x-axis by a factor of a.
Increasing the value of a will make the graph seem taller; however, increasing the value of b will make the graph seem narrower, not wider.
Why is one of these factors a reciprocal while the other factor is not? Thinking of a stretch in terms of multiplying x and y in y = f(x) by constants r and s gives ry = f(sx). Isolating y results in the equation 
. When written in this form, the vertical stretch is by a factor of 
and the horizontal stretch is by a factor of 
. Typically 
is written as a and s is written as b to give the more familiar y = af(bx).
“Example 2” on pages 21 and 22 of the textbook explains how a affects the graph of y = af(x). If you would like more explanation, read “Example 2.” If you are comfortable with the changes caused by a, try Self-Check 1.
Complete “Your Turn” from “Example 2” on page 22 of the textbook. Answer
“Example 3” on pages 23 and 24 of the textbook explains how b affects the graph of y = f(bx). If you would like more explanation, read “Example 3.” If you are comfortable with the changes caused by b, try Self-Check 2.
Complete “Your Turn” from “Example 3” on page 24 of the textbook. Answer
Now you have seen how to graph a function of the form y = af(x) and y = f(bx) given y = f(x). In the next example, a and b will be combined in a function in the form y = af(bx). Watch Graphing y = af(bx) to see how to graph y = af(bx) from y = f(x).
