Exercise 28 Page 160

To graph the functions without going through the entire process of transforming the parent function, we can make two tables of values. Then, we only need to plot and connect the obtained points and compare the graphs.

Graph

Let's begin with creating a table of values of function $h (x) .$

$x$	$∣ x + 5 ∣$	Simplify	$h (x)$
$- 5$	$∣ - 5 + 5 ∣$	$∣ 0 ∣$	$0$
$- 3$	$∣ - 3 + 5 ∣$	$∣ 2 ∣$	$2$
$- 1$	$∣ - 1 + 5 ∣$	$∣ 4 ∣$	$4$
$1$	$∣ 1 + 5 ∣$	$∣ 6 ∣$	$6$

Now let's do the same with function $t (x) .$

$x$	$∣ 2 x + 5 ∣$	Simplify	$t (x)$
$- 5$	$∣ 2 (- 5) + 5 ∣$	$∣ - 5 ∣$	$5$
$- 3$	$∣ 2 (- 3) + 5 ∣$	$∣ - 1 ∣$	$1$
$- 1$	$∣ 2 (- 1) + 5 ∣$	$∣ 3 ∣$	$3$
$1$	$∣ 2 (1) + 5 ∣$	$∣ 7 ∣$	$7$

Finally, we can plot these ordered pairs on one coordinate plane.

Comparison

We can rewrite $t (x)$ as $h (2 x),$ which is a horizontal shrink of $h (x)$ by a factor of $\frac{1}{2} .$ It is being shrunk closer the $y -$ axis. Note that when the $x -$ values of $f$ are two times the $x -$ values of $g,$ the $y -$ values stay the same.