AnswersSummer 2026 Common Core Algebra I - MA3109 B-IC MEF22QXVReflections of Exponential Functions

Translations of Exponential Functions Answers

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1
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The graphs of f(x) = 5x and its translation, g(x), are shown on the graph.

Question illustration
A
g(x) = 5x – 9
B
g(x) = 5x – 10
C
g(x) = 5x – 9
D
g(x) = 5x – 10
2
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Which is the graph of g(x) = 2x – 1 + 3?

A
On a coordinate plane, an exponential function has a horizontal asymptote at y = 3 and crosses the y-axis at (0, 4).
Option A
B
On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 3 and crosses the y-axis at (0, negative 2)
Option B
C
On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 1 and crosses the y-axis at (0, 7).
Option C
D
On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 1 and crosses the y-axis at (0, negative 1).
Option D
3

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

Question illustration
A
−2
B
−1
C
1
D
2
4

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}
5

Which set of steps will translate f(x) = 6x to g(x) = 6x – 5 – 7?

A
Shift f(x) = 6x five units to the left and seven units up.
B
Shift f(x) = 6x five units to the right and seven units down.
C
Shift f(x) = 6x seven units to the right and five units up.
D
Shift f(x) = 6x seven units to the left and five units down.
6

What is the range of f(x) = 3x + 9?

{
{y | y < 9}
{
{y | y > 9}
{
{y | y > 3}
{
{y | y < 3}
7

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.
8

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.
9

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
10

What are the domain, range, and asymptote of h(x) = (1.4)x + 5?

d
domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5
d
domain: {x | x > 5}; range: {y | y is a real number}; asymptote: y = 5
d
domain: {x | x > –5}; range: {y | y is a real number}; asymptote: y = –5
d
domain: {x | x is a real number}; range: {y | y > –5}; asymptote: y = –5

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