Dugopolski’s 25College Algebra
Chapter 2 Test — Form A Name: _________________________
Determine whether each equation defines as a function of .
1. 2. | | 3 = 2 = 2 + 1
1. ___________ 2. ___________
State the domain and range of each relation.
3. 4. = |2 3| =
3. 4. domain: ____________ domain:____________
range:______________ range:______________
Sketch the graph of each function.
5. 6. =
7. 8. ( ) =
Let ( ) = and ( ) = . Find and simplify each of the following expressions.
9. 10. 11. 12. ( 4) ( ) ( )(2)
9. __________ 10. __________ 11. __________ 12. __________
26 Form 2A
Solve each problem.
13. State the intervals on which is increasing.
13. ___________________________
14. Discuss the symmetry of the graph of the function
14. ___________________________
15. State the solution set to the inequality using interval notation.
15. ___________________________
16. Pete’s Print Shop charges $60 for printing 300 business cards and $80 for printing
500 business cards. What is the average rate of change of the cost of printing as the
number of cards goes from 300 to 500?
16. ___________________________
17. The area of a rectangle is 30 square feet. Write the perimeter of this rectangle as a
function of the length of one of its sides, .
17. ___________________________
18. The grade on Walker’s math test varies directly with the number of hours he spends
studying for the test. If he studies only 2 hours, he makes a 62. What will his score be
if he studies for 3 hours?
18. ___________________________
Dugopolski’s 27College Algebra
Chapter 2 Test — Form B Name: _________________________
Determine whether each equation defines as a function of .
1. 2.
1. ___________ 2. ___________
State the domain and range of each relation.
3. 4.
3. 4. domain: ____________ domain:____________
range:______________ range:______________
Sketch the graph of each function.
5. 6.
7. 8. ( ) =
Let ( ) and ( ) . Find and simplify each of the following.
9. 10. 11. 12. ( ) ( ) ( )( )
9. __________ 10. __________ 11. __________ 12. __________
28 Form 2B
Solve each problem.
13. State the intervals on which is increasing.
13. ________________________
14. Discuss the symmetry of the graph of the function
14. ________________________
15. State the solution set to the inequality using interval notation.
15. ________________________
16. Pete’s Print Shop charges $50 for printing 500 business cards and $90 for printing
1000 business cards. What is the average rate of change of the cost of printing as the
number of cards goes from 500 to 1000?
16. ________________________
17. The perimeter of a rectangle is 10 square feet. Write the area of this rectangle as a
function of the length of one of its sides, .
17. ________________________
18. The grade on Walker’s math test varies directly with the number of hours he spends
studying for the test. If he studies only 2 hours, he makes a 50. What will his score be
if he studies for 3 hours?
18. ________________________
Dugopolski’s 29College Algebra
Chapter 2 Test — Form C Name:_________________________
Determine whether each relation defines as a function of .
1. 2.
1. ___________ 2. ___________
State the domain and range of each relation.
3. 4. ( ) =
3. 4. domain: ____________ domain:____________
range:______________ range:______________
Sketch the graph of each function.
5. 6.
7. 8.
Let ( ) and ( ) . Find and simplify each of the following.
9. 10. 11. 12. ( ) ( )( )
9. __________ 10. __________ 11. __________ 12. ________________
30 Form 2C
Solve each problem.
13. State the intervals on which | 2 | 3 is increasing.
13. ___________________________
14. Let ( ) = 2, ( ) = and ( ) = 1. Write ( ) = 2 + 1 as a
composition of appropriate functions chosen from , , and .
14. ___________________________
15. State the solution set to the inequality using interval notation.
15. ___________________________
16. Jane’s Advertising charges $500 for 1200 flyers and $780 for 1600 flyers. What is the
average rate of change of the cost of the advertising as the number of flyers goes from
1200 to 1600?
16. ___________________________
17. Write the area of a square as a function of the length of one of its diagonals, .
17. ___________________________
18. The cost of constructing a 5-foot by 7-foot deck is $192.50. If the cost varies jointly as
the length and width, then what does an 8-foot by 10-foot deck cost?
18. ___________________________
Dugopolski’s 31College Algebra
Chapter 2 Test — Form D Name:_________________________
Determine whether each relation defines as a function of .
1. 2.
1. ___________ 2. ___________
State the domain and range of each relation.
3. 4. ( ) =
3. 4. domain: ____________ domain:____________
range:______________ range:______________
Sketch the graph of each function.
5. 6.
7. 8.
Let ( ) and ( ) . Find and simplify each of the following.
9. 10. 11. 12. ( ) ( )( )
9. __________ 10. __________ 11. __________ 12. ________________
32 Form 2D
Solve each problem.
13. State the intervals on which 2 is increasing.
13. ___________________________
14. Let ( ) = , ( ) = and ( ) = . Write ( ) = as a
composition of appropriate functions chosen from , , and .
14. ___________________________
15. State the solution set to the inequality using interval notation.
15. ___________________________
16. Jane’s Advertising charges $500 for 1200 flyers and $820 for 1600 flyers. What is the
average rate of change of the cost of the advertising as the number of flyers goes from
1200 to 1600?
16. ___________________________
17. Write the area of a square as a function of the length of one of its diagonals, .
17. ___________________________
18. The cost of constructing a 5-foot by 7-foot deck is $148.75. If the cost varies jointly as
the length and width, then what does an 8-foot by 10-foot deck cost?
18. ___________________________
Dugopolski’s 33College Algebra
Chapter 2 Test — Form E Name:_________________________
Multiple Choice: Choose the best answer for each of the following.
_____ 1. Which of the following define as a function of ?
A. C. E.
B. D. F.
a. A, B, E b. A, C, E c. B, D, F d. A, B, F
_____ 2. What is the range of the relation: ?
a. [ 1, ) b. [0, ) c. [1, ) d. ( )
_____ 3. Find , if and .
a. b. c. d. 6
_____ 4. Determine the range of .
a. [1, ) b. ( ) c. ( 0) (0, ) d. [1, 2)
_____ 5. Explain how to use the graph of to get the graph of
a. Translate 2 units left c. Translate 2 units right
b. Translate 2 units down d. Translate 2 units up
_____ 6. Solve the inequality by using its graph.
a. ( , 3] b. [ 1, 3] c. ( , 1] [3, ) d.[3, )
_____ 7. Find the domain of if {( 1, 0), ( 2, 4), (3, 6)}
and {( 1, 0), (0, 5), (3, 2)}.
a. { 1, 3} b. { 1, 2, 0, 3} c. { 1, 0, 3} d. { 1, 2, 3}
_____ 8. If and , find .
a. 0 b. 2 c. d. undefined
_____ 9. The area of a rectangle is 20 square feet. Write the perimeter of this
rectangle as a function of the length of of its sides, .one
a. c.
b. d.
34 Form 2E
_____ 10. Use to find the range of .
a. ( , 3) ( 3, ) c. ( , 2) (2, )
b. ( , 0) (0, ) d. ( , ) ( , )
_____ 11. Express the radius of a circle, , as a function of its circumference ,
given , where is the diameter of the circle.
a. b. c. d.
_____ 12. Find the constant of variation for the following: varies inversely as the
square of and when .
a. 20 b. 100 c. d.
_____ 13. Write a formula with the appropriate variation constant that describes the
variation of the length of a building in yards ( ) with the length of a
building in inches ( ).
a. b. c. d.
_____ 14. Find if and .
a. b. c. d. and 3
_____ 15. If a function is even, then it is:
a. level c. symmetric to the –axis
b. not invertible d. symmetric to the origin
_____ 16. If = , find .
a. b. c. d.
_____ 17. Determine the symmetry of the graph of ( ) = .
a. Symmetric to the -axis c. Symmetric to the origin
b. Symmetric to d. No symmetry
_____ 18. Jane’s Advertising charges $500 for 1200 flyers and $780 for 1800 flyers.
What is the average rate of change of the cost of the advertising as the
number of flyers goes from 1200 to 1800?
a. $280.00 b. $0.23 c. $0.16 d. $0.47
Dugopolski’s 35College Algebra
Chapter 2 Test — Form F Name:_________________________
Multiple Choice: Choose the best answer for each of the following.
_____ 1. Which of the following define as a function of ?
A. C. E.
B. D. F.
a. B, D, F b. A, C, E c. A, B, F d. A, B, E
_____ 2. What is the range of the relation: ?
a. [ 1, ) b. [0, ) c. [1, ) d. ( )
_____ 3. Find , if and .
a. 13 b. 0 c. undefined d. 7
_____ 4. Determine the range of ( ) =
a. ( ) , ) b. ( ) c. [1, ) d. , )
_____ 5. Explain how to use the graph of to get the graph of .
a. Translate 2 units left c. Translate 2 units right
b. Translate 2 units down d. Translate 2 units up
_____ 6. Solve the inequality by using its graph.
a. ( , 1] b. [1, 3] c. ( , 3] [1, ) d.[ 3, 1]
_____ 7. Find the domain of if {( 1, 0), ( 2, 4), (3, 6)}
and {( 1, 0), (0, 5), (3, 2)}.
a. { 1, 2, 3} b. { 1, 2, 0, 3} c. { 1, 0, 3} d. { 1, 3}
_____ 8. If and , find .
a. b. c. d.
_____ 9. The area of a rectangle is square feet. Write the perimeter of this
rectangle as a function of the length of of its sides, .one
a. c.
b. d.
36 Form 2F
_____ 10. Use to find the range of .
a. ( , 3) (3, ) c. ( , 2) (2, )
b. ( , 0) (0, ) d. ( , ) ( , )
_____ 11. Express the radius of a circle, , as a function of its circumference , given
, where is the diameter of the circle.
a. b. c. d.
_____ 12. Find the constant of variation for the following: varies inversely as the
cube of and when .
a. 100 b. c. d.
_____ 13. Write a formula with the appropriate variation constant that describes the
variation of the length of a building in yards ( ) with the length of a
building in inches ( ).
a. b. c. d.
_____ 14. Find if and .
a. b. c. d. and
_____ 15. If a function is even, then it is:
a. level c. not invertible
b. symmetric to the -axis d. symmetric to the origin
_____ 16. If , find .
a. b. c. d.
_____ 17. Determine the symmetry of the graph of ( ) = .
a. Symmetric to the -axis c. Symmetric to the origin
b. Symmetric to d. No symmetry
_____ 18. Jane’s Advertising charges $500 for 1200 flyers and $780 for 1800 flyers.
What is the average rate of change of the cost of the advertising as the
number of flyers goes from 1200 to 1800?
a. $0.16 b. $0.47 c. $280.00 d. $0.23
Dugopolski’s 115College Algebra
Chapter Test Keys
CHAPTER 2
116 Chapter 2 Test Key