AnswersCommon Core Algebra I - MA3109 A-ICPerformance Task: Construct and Analyze Piecewise 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) = 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
3

What is the domain of f(x) = 5x – 7?

{
{x | x > –7}
{
{x | x < –7}
{
{x | x > 0}
{
{x | x is a real number}
4

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

Question illustration
A
−2
B
−1
C
1
D
2
5

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}
6

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

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

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
8

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
9

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
10

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

Question illustration
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

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