AnswersHigh School Math 2 AExponential Growth Functions

Lesson 6.9: Translations of Exponential Functions Answers

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What are the domain, range, and asymptote of h(x) = 2x + 4?

A
domain: {x | x > 0}; range: {y | y is a real number}; asymptote: y = 0
B
domain: {x | x > –4}; range: {y | y is a real number}; asymptote: y = –4
C
domain: {x | x is a real number}; range: {y | y > 0}; asymptote: y = 0
D
domain: {x | x is a real number}; range: {y | y > 0}; asymptote: y = –4
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

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

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

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.
5

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
6

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
7

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
8

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
9

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
10

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

A
domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5
B
domain: {x | x > 5}; range: {y | y is a real number}; asymptote: y = 5
C
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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