Page 528 - Algebra 1

Example
4
Application: Soccer
The Soccer Administration plans to have 64 regular players on a team. The players will be divided equally among the coaches. There will be one backup player placed on each team at the beginning of the season in addition to the regular players. The number of players on each team, y, is given by
a. Determine the vertical and horizontal asymptotes of the function. SOLUTION
y = _64 + 1, where x is the number of coaches. x
Hint
When a rational function has no value for b in
a
y = _x - b + c, the vertical
asymptote is the y-axis or x = 0.
_
y= 64 +1 a=64,b=0,andc=1
x
The equation of the horizontal asymptote is y = 1. The equation of the vertical asymptote is x = 0.
b. If there are 4 coaches, how many players will each team have? SOLUTION
_
y = 64 + 1 x
_
y= 64 +1
Replacexwith4.
Divide 64 by 4 and then add 16 + 1.
There will be 17 players on each team.
Find the excluded values.
(Ex 1) _4 a. y = 6m
Identify th_e asymptotes. (Ex 2)
4 d. y = x + 1
4 y = 17
Lesson Practice
6m _
m-3 _
b. y = m + 2
e. y = x + 7 + 6
Identify the asymptotes and graph each function.
f. y = _6 g. y = _1 - 5.
(Ex 3) x + 4 (Ex 3) x - 6
A golf instructor has a budget of $5500 to buy new demonstration clubs. He
will receive 5 free clubs whe_n he places his order. The number of clubs, y, that
5500
he can buy is given by y = x + 5, where x is the price per club.
(Ex 4)
h. Determine the vertical and horizontal asymptotes of the function. i. If each club costs $100, how many clubs will he receive?
2 _
c. y = 4m - 8
Lesson 78 513