Download Name Date Class Rational Functions Module Quiz: B Original

Name _______________________________________ Date __________________ Class __________________
MODULE
8
Rational Functions
Module Quiz: B
For 1–2, build a rational model, f(x) for
each situation. Then solve the model for
the given value of x.
4. Does each set of data represent an
inverse variation?
A
1. Sara and her friends are going on a day
trip to the fair. The total cost for taking
the train is $178.75, and the cost of each
fair ticket is $15. How much does the trip
cost per person if 5 people go?
B
_______________________________________
C
2. A social studies class is taking a field trip
to the history museum. The cost for
renting a bus is $250, and the entry fee for
the museum is $8.75 per person. To the
nearest cent what is the cost per person if
21 people go?
D
3. Choose True or False for each statement
(2 x  3)
.
about the function f ( x ) 
(2 x  7)
B f (x) 
True
0.75
3
7.5
x
1.5
3
5
y
5
2.5
1.5
x
10
20
25
y
0.1
0.5
4
x
0.3
0.4
0.6
y
10
7.5
5
True
Yes
No
Yes
No
Yes
No
Yes
No
False
False
C The graph has a horizontal
asymptote at y  1.5.
False
7
.
3
True
False
D The graph has a vertical asymptote
at x  3.5.
False
7
D f(x) has a vertical asymptote at  .
2
True
y
B The graph has a vertical asymptote
at x  1.5.
False
C f(x) has a vertical asymptote at
5
True
1 9
(3 x  7)
True
2
A The graph has a horizontal
asymptote at y  3.5.
1 4
(2 x  7)
True
0.5
5. Choose True or False for each statement
about the graph of the rational function
3x  4
f (x) 
.
2x  7
_______________________________________
A f (x) 
x
True
False
6. Membership in a fitness club costs $45
per month plus a one-time registration
fee of $102. Write a rational function for
the average monthly cost of an x-month
membership in the club. Then find the
average monthly cost of membership if
a member leaves after 6 months.
False
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
43
Name _______________________________________ Date __________________ Class __________________
MODULE
8
Rational Functions
Module Quiz: B
7. Identify the horizontal and vertical
asymptotes of the function
1
f (x) 
 3. Then graph the
3x  6
function.
11. Find the domain and range.
________________________________________
12. Describe the end behavior.
________________________________________
13. Sketch the graph of the function.
_______________________________________
8. Write the function graphed below in the
a
form f ( x ) 
 k.
xh
14. Li Ming rowed 2 miles upstream and then
3 miles downstream. His average speed
rowing in still water is 2 miles per hour.
The model that describes the situation is
2
3
s  10
f (s ) 


2  s 2  s (2  s )(2  s )
where s is the average speed of the
current and f(s) is the total amount of
time that Li Ming rowed. Sketch a graph
of the function and use it to determine the
average speed of the current if Li Ming
rowed for 3 hours.
_______________________________________
For 9–13, use the rational function
x 2  x  12
f (x)  2
.
x  3x  4
9. Find the vertical asymptote(s).
_______________________________________
10. Find the point(s) of discontinuity.
________________________________________
_______________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
44
Name _______________________________________ Date __________________ Class __________________
13.
14. A
15. f ( x )  x 3  39x  70
16. f ( x )  x 3  5x 2  9x  45
17. f ( x )  x 4  9x 2  112
18. 4i, 1, 1
19. 3, 3i
1
20.  , 1, 2
3
14.
MODULE 8 Rational Functions
Module 8 Quiz B
1. f ( x ) 
178.75
 15; $50.75
x
250
 8.75; $20.65
x
3. A True B False C False D True
2. f ( x ) 
4. A No B Yes C No D Yes
1 mi/hr
5. A False B False C True D True
Module 8 Quiz Modified
102
6. f ( x ) 
 45; $62
x
7. y  3, x  2;
1. C
2. B
3. f ( x ) 
33
7
x
4. $18
5. Domain (, 3), (3, ); Range (, 2),
(2, )
6. B
7. A
8. y  1, x  2;
8. f ( x ) 
4
3
x 2
9. x  1
7

10. 4, 
5

11. domain x | x  4,1, range
7

 y | y  1, 
5

12. as x  , f ( x )  1 , as x  ,
f (x)  1
9. B
10. $16
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
45