Exercise 19 Page 736

We are told that Katelyn paid $\$38$ for pizza and soda for her study group. The cost per person $y$ can be found using the given function. In this function, $x$ is the number of the people in the study group. Note that this is a rational function. To graph it, let's make a table of values. We will exclude non-positive values since the number of people cannot be negative or zero.

$x$	$\frac{38}{x}$	$y$
$1$	$\frac{38}{1}$	$38$
$2$	$\frac{38}{2}$	$19$
$5$	$\frac{38}{5}$	$7.6$
$10$	$\frac{38}{10}$	$3.8$
$19$	$\frac{38}{19}$	$2$
$38$	$\frac{38}{38}$	$1$

Now, we can plot the obtained points and connect them with a smooth curve to graph the given function.

Note that as $x$ increases, $y$ approaches $0.$ This is reasonable because, as the number of people increases, the cost per person gets closer to $0.$ Therefore, the horizontal asymptote is at $y=0.$ Additionally, looking at the graph, we can observe that there is also a vertical asymptote at $x=0.$