AnswersSummer 2026 Common Core Algebra I - MA3109 B-IC MEF22QXVExponential Decay Functions

Translations of Exponential Functions Answers

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1
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Which steps will translate f(x) = 3x to g(x) = 3x + 1 + 4?

A
Shift f(x) = 3x one unit up and four units to the right.
B
Shift f(x) = 3x one unit up and four units to the left.
C
Shift f(x) = 3x one unit to the right and four units up.
D
Shift f(x) = 3x one unit to the left and four units up.
2
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The graphs of f(x) = 10x and its translation, g(x), are shown.

Question illustration
A
g(x) = 10x – 3
B
g(x) = 10x + 3
C
g(x) = 10x – 3
D
g(x) = 10x + 3
3

Which is the graph of g(x) = (0.5)x + 3 – 4?

A
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, negative 4).
Option A
B
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 3. It crosses the y-axis at (0, 3).
Option B
C
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, 4).
Option C
D
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 4. It crosses the y-axis at (0, 12).
Option D
4

The graph shows f(x) = and its translation, g(x).

Question illustration
A
translation of four units up
B
translation of five units up
C
translation of four units to the right
D
translation of five units to the right
5

The graph of g(x) is the result of translating the graph of f(x) = three units to the left. What is the equation of g(x)?

Question illustration
A
g(x) =
Option A
B
g(x) =
Option B
C
g(x) =
Option C
D
g(x) =
Option D
6

f(x) = 7x g(x) = 7x + 6

A
The domain of g(x) is {x | x > 6}, and the domain of f(x) is {x | x > 0}.
B
The domain of g(x) is {y | y > 0}, and the domain of f(x) is {y | y > 6}.
C
The asymptote of g(x) is the asymptote of f(x) shifted six units down.
D
The asymptote of g(x) is the asymptote of f(x) shifted six units up.
7

What is the domain of f(x) = 3x – 2?

A
{x | x > 0}
B
{x | x < 0}
C
{x | x = 0}
D
{x | x is a real number}
8

What are the domain, range, and asymptote of h(x) = (0.5)x – 9?

A
domain: {x | x > 9}; range: {y | y is a real number}; asymptote: y = 9
B
domain: {x | x > –9}; range: {y | y is a real number}; asymptote: y = –9
C
domain: {x | x is a real number}; range: {y | y > 9}; asymptote: y = 9
D
domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9
9

The graph shows that is translated horizontally and vertically to create the function .

Question illustration
A
−2
B
−1
C
1
D
2
10

What is the domain of f(x) = 5x – 7?

A
{x | x > –7}
B
{x | x < –7}
C
{x | x > 0}
D
{x | x is a real number}

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