Name: 
 

Multiplying, Dividing and Composing Functions


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Look at the functions below.

f(x) = (2x + 1) – 5
g(x) = (4x – 7) + 3

Which of the following is the equation of the combined functions h(x) = f(x) Ÿ g(x)?
A.
h(x) = 8x2 – 10x – 7
B.
h(x) = 8x2 – 24x + 16
C.
h(x) = 8x2 + 24x + 16
D.
h(x) = 8x2 + 8x – 16
 

 2. 
A car drives at a constant speed of 60 mph. The car averages 15 miles per gallon of gas. If h represents the number of hours the car has been driven, which of the following represents the composed function rule that can be used to calculate the number of gallons of gasoline used in h hours?
A.
mc002-1.jpg
B.
15(60h)
C.
60h + 15
D.
mc002-2.jpg
 

 3. 
If f(x) = 3x + 5 and g(x) = x2 – 4, what is f(g(x))?
A.
3x3 + 5x2 – 12x – 20
B.
x2 + 3x + 1
C.
3x2 – 7
D.
9x2 + 30x + 21
 

 4. 
A gas pump at a convenience store can pump gasoline into a car at a rate of 3 gallons per minute. The convenience store charges $2.15 per gallon for gas. The mapping below shows the amount of revenue the convenience store receives based on the number of minutes the gas pump has been pumping gas.

mc004-1.jpg

Which of the following statements is NOT true about the situation?
A.
The domain of f(x) is the same as the range of g(x).
B.
The range of f(x) depends on the number of seconds the pump has been pumping gas.
C.
The domain of g(x) is the same as the range of f(x).
D.
The amount of revenue depends on the number of seconds the pump has been pumping gas.
 

 5. 
Look at the table below.

x
f(x)
g(x)
h(x)
-3
-3
-1
3
-2
-1
1
-1
-1
1
3
3
0
2
5
10
1
5
7
35
2
7
9
63
3
9
11
99

Which of the following correctly describes the relationship between f(x), g(x), and h(x)?
A.
h(x) = f(x) – g(x)
B.
h(x) = f(x) Ÿ g(x)
C.
h(x) = f(x) + g(x)
D.
None of the above
 

 6. 
Which of the following is not true about the quotient of two polynomial functions?
A.
A quadratic function divided by a cubic function generates a linear function.
B.
A cubic function divided by a quadratic function generates a linear function.
C.
A linear function divided by a quadratic function generates a rational function.
D.
A quadratic function divided by a linear function generates a linear function.
 

 7. 
Look at the functions below.

f(x) = (3x – 1)2 + 4
g(x) = (3x – 2) + 1

Which of the following is the equation of the separated functions h(x) = f(x) Ÿ g(x)?
A.
h(x) = 27x3 – 9x2 – 9x + 1
B.
h(x) = 27x3 – 9x2 + 9x + 5
C.
h(x) = 27x3 – 27x2 + 21x – 5
D.
h(x) = 27x3 – 27x2 + 3x – 1
 

 8. 
If f(x) = x + 1.5 and g(x) = 5x2, what is g(f(x))?
A.
g(f(x)) = 5x2 + 15x + 2.25
B.
g(f(x)) = 5x3 + 7.5x2
C.
g(f(x)) = 5x2 + 11.25
D.
g(f(x)) = 5x2 + 15x + 11.25
 

 9. 
Use the graph, f(x) = x2 – 4, and g(x) = x + 2 to determine values for h(x) = f(x) ÷ g(x) and write the equation for h(x).

mc009-1.jpg

x
–3
–1
1
3
f(x)
    
g(x)
    
h(x)
    

A.
h(x) = –2x – 2
B.
h(x) = x + 2
C.
h(x) = x – 2
D.
h(x) = 2x – 5
 

 10. 
Which of the following best represents the function h(x)?

x
f(x)
g(x)
h(x)
0
-1
1
-1
1
8
2
4
2
27
3
9
3
56
4
14
4
95
5
19
5
144
6
24

A.
h(x) = f(x)¸g(x)
B.
h(x) = g(x)¸f(x)
C.
h(x) = g(x) + f(x)
D.
h(x) = f(x) + g(x)
 

 11. 
Use the table for the functions f(x) and g(x) to find the values for the quotient h(x) = f(x) ÷ g(x).  Then use finite differences to write the function rule for h(x).

x
–2
–1
0
1
2
f(x) = 2x2 + 5x – 3
–5
–6
–3
4
15
g(x) = x + 3
1
2
3
4
5
h(x)
     

A.
h(x) = 2x – 5
B.
h(x) = 2x – 3
C.
h(x) = 2x
D.
h(x) = 2x – 1
 

 12. 
The table below shows values for three functions. 

x
f(x)
g(x)
h(x)
1
-8
2
-4
2
-4
4
-1
3
12
6
2
4
40
8
5
5
80
10
8
6
132
12
11

Which of the following is not true about the functions represented in the table above?
A.
h(x) = f(x)¸ g(x)
B.
g(x) = 2x
C.
f(x) = 6x2 – 14
D.
h(x) = 3x – 7
 

 13. 
Find h(x) = f(x) ÷ g(x) and j(x) = g(x) ÷ f(x) for f(x) = 3x2 + 2x – 8 and g(x) = x + 2.
A.
h(x) = 3x – 4; j(x) = mc013-1.jpg
B.
h(x) = 3x – 4; j(x) = mc013-2.jpg
C.
h(x) = 3x + 4; j(x) = mc013-3.jpg
D.
h(x) = 3x + 4; j(x) = mc013-4.jpg
 

 14. 
A gas pump at a convenience store can pump gasoline into a car at a rate of 3 gallons per minute. The convenience store charges $2.15 per gallon for gas. The mapping below shows the amount of revenue the convenience store receives based on the number of minutes the gas pump has been pumping gas.

mc014-1.jpg

Which of the following represents g(f(x)?
A.
mc014-2.jpg
B.
mc014-3.jpg
C.
g(f(x)) = 2.15 + 3x
D.
g(f(x)) = 2.15(3x)
 

 15. 
Look at the functions below.

f(x) = -2(x – 3)2 – 5
g(x) = 2(x – 3) + 5

Which of the following is the equation of the combined functions h(x) = f(x) Ÿ g(x)?
A.
h(x) = -4x3 + 26x2 – 58x + 23
B.
h(x) = -4x3 – 22x2 + 34x – 23
C.
h(x) = -4x3 – 26x2 + 58x – 23
D.
h(x) = -4x3 + 22x2 – 34x – 23
 

 16. 
Use the graph and values for f(x) = x3 – 6x2 + 11x – 6 and g(x) = x2 – 4x + 3 to complete the values for h(x) = f(x) ÷ g(x) in the table. Choose the equation representing the values for function h(x) = f(x) ÷ g(x).

mc016-1.jpg

x
0
2
4
h(x)
   

A.
h(x) = 2x + 1
B.
h(x) = x + 1
C.
h(x) = x – 2
D.
h(x) = 2x
 

 17. 
If r(x) = x – 7, and q(x) = x 2 – 49, which of the following tables represents h(x) = r(x)¸q(x)?
A.
mc017-1.jpg
B.
mc017-2.jpg
C.
mc017-3.jpg
D.
 mc017-4.jpg
 

 18. 
The graph of the functions f(x) = 4(x – 2)2 – 8 and g(x) = mc018-1.jpg(8x – 12) are graphed below.

mc018-2.jpg

Which of the graphs below represents the combined functions h(x) = f(x) Ÿ g(x)?
A.
mc018-3.jpg
B.
mc018-4.jpg
C.
mc018-5.jpg
D.
mc018-6.jpg
 

 19. 
An electrician charges $45 per hour, h, to install wiring in a house with a supply fee of $250. During the first week of each month he offers a 20% discount. Which of the following represents the composed function rule he could use to calculate his bill during the first week of each month?
A.
0.2(45h + 250)
B.
0.8(45h + 250)
C.
45(0.8h) + 250
D.
45(0.2h) + 250
 

 20. 
Which function shows the quotient w(x) = f(x) ¸ q(x), when f(x) = x – 8 and q(x) = 2x2 – 15x – 8?
A.
mc020-1.jpg
B.
mc020-2.jpg
C.
w(x) =  2x + 1
D.
w(x) =  x – 8
 



 
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