What do the variables x and y represent in the given function?
A
a
See solution.
B
b
See solution.
Practice makes perfect
a
We will graph the function that shows the average number of pages that Trina reads every day from a 300-page book.
y=300/x
In this function x represents the number of days that she reads. To graph the function we will make a table of values.
x
30
20
10
5
y
10
15
30
60
By plotting these points we will draw the graph of the function. Notice that the number of pages that are read and the number of days cannot be negative.
Now we will identify the asymptotes of the function. When the denominator of a rational expression is zero, the expression is undefined.
x= 0 ⇒ 300/0= undefined
The function has a vertical asymptote at x=0. As the average number of pages read each day increases, the number of days she reads gets closer to zero. Besides, since 300x cannot be equal to zero, it has a horizontal asymptote at y=0. As the number of days she reads increases the average number of pages read each day gets closer to zero.
b
Let's arbitrarily take a point from the graph that we drew in Part A.
It means that if she reads the book for 20 days, the average number of pages that she reads each day will be 15.
