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=x38
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
x38
y
1
138
38
2
238
19
5
538
7.6
10
1038
3.8
19
1938
2
38
3838
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=x38
However, in our case, we connected the points with a smooth curve to describe the horizontal and vertical asymptotes.
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