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.

y = \frac{3 8}{x}

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.

$x$	$\frac{3 8}{x}$	$y$
$1$	$\frac{3 8}{1}$	$38$
$2$	$\frac{3 8}{2}$	$19$
$5$	$\frac{3 8}{5}$	$7.6$
$10$	$\frac{3 8}{1 0}$	$3.8$
$19$	$\frac{3 8}{1 9}$	$2$
$38$	$\frac{3 8}{3 8}$	$1$

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 .

Extra

Discontinuous function

Recall that

x

is the number of people in the study group. Therefore, the cost function is a discontinuous function because it is defined only for integer values of

x .

y = \frac{3 8}{x}

However, in our case, we connected the points with a smooth curve to describe the horizontal and vertical asymptotes.

Exercise

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