Recognizing a Horizontal Compression on a Graph

Relate the function $g (x)$ to $f (x)$ in Figure 26.

Figure 26

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The graph of $g (x)$ looks like the graph of $f (x)$ horizontally compressed. Because $f (x)$ ends at $(6, 4)$ and $g (x)$ ends at $(2, 4),$ we can see that the $x -$ values have been compressed by $\frac{1}{3},$ because $6 (\frac{1}{3}) = 2.$ We might also notice that $g (2) = f (6)$ and $g (1) = f (3) .$ Either way, we can describe this relationship as $g (x) = f (3 x) .$ This is a horizontal compression by $\frac{1}{3} .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write a formula for the toolkit square root function horizontally stretched by a factor of 3.

How did it go?