Answers2627 ALGEBRA II AFunction Operations

Function Operations Answers

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The graphs of f(x) and g(x) are shown below. Which of the following is the graph of (g – f)(x)?

Question illustration
A
On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)
Option A
B
On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).
Option B
C
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
Option C
D
On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).
Option D
2
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If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be true?

Question illustration
A
The leading coefficients of f(x) and g(x) are opposites.
B
The leading coefficients of f(x) and g(x) are opposite reciprocals.
C
The leading coefficients of f(x) and g(x) are the same.
D
The leading coefficients of f(x) and g(x) are reciprocals.
3

The graphs of f(x) and g(x) are shown below. For what interval is the value of (f – g)(x) negative?

Question illustration
A
(negative infinity, negative 1)
Option A
B
(negative infinity, 2)
Option B
C
(0, 3)
Option C
D
(2, infinity)
Option D
4

Which expression is equivalent to (st)(6)?

A
s(t(6))
B
s(x) × t(6)
C
s(6) × t(6)
D
6 × s(x) × t(x)
5

If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?

A
12
B
14
C
36
D
38
6

If f(x) = 16x – 30 and g(x) = 14x – 6, for which value of x does (f – g)(x) = 0?

A
–18
B
–12
C
12
D
18
7

If and d(x) = x + 3, what is the domain of (cd)(x)?

Question illustration
A
all real values of x
B
all real values of x except x = 2
C
all real values of x except x = –3
D
all real values of x except x = 2 and x = –3
8

Which expression is equivalent to ?

Question illustration
A
f (5) times g (5)
Option A
B
f (5) + g (5)
Option B
C
5 f (5)
Option C
D
5 g (5)
Option D
9

Which expression is equivalent to (f + g)(4)?

A
f(4) + g(4)
B
f(x) + g(4)
C
f(4 + g(4))
D
4(f(x) + g(x))
10

If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

A
–4
B
–2
C
2
D
4
11

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

A
6 – 3 – (4 + 3)2
B
6 – 3 – (4 – 32)
C
6(3) – 4 + 32
D
6(3) – 4 – 32
12

If f(x) = 3 – 2x and , what is the value of ?

Question illustration
A
–169
B
–1
C
13
D
104
13

If r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to ?

Question illustration
A
StartFraction 3 (6) minus 1 Over 2 (6) + 1 EndFraction
Option A
B
StartFraction (6) Over 2 (6) + 1 EndFraction
Option B
C
StartFraction 36 minus 1 Over 26 + 1 EndFraction
Option C
D
StartFraction (6) minus 1 Over (6) + 1 EndFraction
Option D
14

If and , what is the value of (f – g)(144)?

Question illustration
A
–84
B
–60
C
0
D
48

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