Exercise 19 Page 736

Make a table of values to graph the given rational function. Then, describe the asymptotes — lines that the graph approaches but never touches — by looking at the graph.

Graph:

Horizontal Asymptote: y=0
Vertical Asymptote: x=0

Practice makes perfect

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 = 38/xIn 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	38/x	y
1	38/1	38
2	38/2	19
5	38/5	7.6
10	38/10	3.8
19	38/19	2
38	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.

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=38/x However, in our case, we connected the points with a smooth curve to describe the horizontal and vertical asymptotes.

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Exercises p.736-738

Exercise 19 Page 736

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