Algebra 1 Common Core Student Edition, Grade 8-9

® ^ Got It? 3. a. What are the asymptotes of the graph of y = j+^3 - 4? Graph

the function.

b. Reasoning Is it possible for two different rational functions to have

the same vertical and horizontal asymptotes? Explain your reasoning.

Using a Rational Function

Dancing Your dance club sponsors a contest at a local reception hall. Reserving a

private room costs $350, and the cost will be divided equally among the people

who enter the contest. Each person also pays a $30 entry fee.

0 What equation gives the total cost per person y of entering the contest as a

function of the number of people x who enter the contest?

Re l at e total cost per person = — c° st of renting private room— + ent ry fee per person

number of people entering contest

Write y J ™x +30

w Pr o b l em 4

Since both y and x must be nonnegative numbers,

use only the part of the graph in the first quadrant.

The equation y = ^ + 30 models the situation.

0 What is the graph of the function in part (A)? Use the graph to describe the

change in the cost per person as the number of people who enter the contest

increases.

Use a graphing calculator to graph y = + 30.

You can see from the graph that as the number of
people who enter the contest increases, the cost
per person decreases. Because the graph has a
horizontal asymptote at y = 30, the cost per person
will eventually approach $30.
0 Approximately how many people must enter the contest in order for the total
cost per person to be about $50?
Th«nk^^
How can you check
the reasonableness
of your answer?
Substitute 18 for x in
the equation you found
in part (A) and simplify.
I f y is approximately
$50, your answer is
reasonable.

Use the key or the TABLE feature. When

y = 50, x = 18. So if 18 people enter the contest, the

cost per person will be about $50.

Go t I t? 4. In Problem 4, suppose the cost to rent a private room increases

to $400. Approximately how many people must then enter the

contest in order for the total cost per person to be about $50?

708 Ch a p t er 11 Rat i o n al Ex p r essi o n s an d Fu n ct i o n s