Graphing Exponential Functions Answers

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21
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How does the graph of y = 3x compare to the graph of y = 3–x?

A
The graphs are the same.
B
The graphs are reflected across the x-axis.
C
The graphs are reflected across the y-axis.
23

Which function is graphed on the right?

A
y = 2x+3 – 2
B
y = 2x–3 + 2
C
y = 2x–2 + 3
D
y = 2x–2 – 3
24

How can you use transformations to graph this function? Explain your steps.

Question illustration
Answer:

To graph the function y = 3 * 7^(-x) + 2, start with the parent exponential function y = 7^x. First, reflect the graph across the y-axis to account for the negative exponent (-x), which changes the function to y = 7^(-x). Next, apply a vertical stretch by a factor of 3, resulting in y = 3 * 7^(-x). Finally, shift the entire graph up 2 units to account for the +2. This transformation changes the horizontal asymptote from y = 0 to y = 2.

25

How does the graph of y = 3–x compare to the graph of

Question illustration
A
The graphs are the same.
B
The graphs are reflected across the x-axis.
C
The graphs are reflected across the y-axis.
26

Which of the following did you include in your response?

A
Sketch the graph of .
B
Reflect the graph across the y-axis to show the function .
C
Stretch the graph vertically by a factor of 3 to show the function
D
Shift the graph up 2 units to show the function
27

Which statements are true about the graph?

A
The graph shows exponential growth.
B
The graph shows exponential decay.
C
The graph shows reflected over the x-axis.
D
The graph shows y = 2x reflected over the y-axis.
28

negative infinityzeropositive infinity

A
negative infinity
B
zero
C
positive infinity
30

0 to infinity3 to infinitynegative infinity to infinity

A
0 to infinity
B
3 to infinity
C
negative infinity to infinity
31

negative infinityzero✔ positive infinity

A
negative infinity
B
zero
C
✔ positive infinity
33

y = 0y = –3y = –5

Question illustration
A
y = 0
B
y = –3
C
y = –5
34

✔ 0 to infinity3 to infinitynegative infinity to infinity

A
✔ 0 to infinity
B
3 to infinity
C
negative infinity to infinity
35

Which statements are true about the graph?

A
The graph shows exponential growth.
B
The graph shows exponential decay.
C
The graph shows reflected over the x-axis.
Option C
D
The graph shows y = 2x reflected over the y-axis.
36

How does the graph of y = 3–x compare to the graph of

Question illustration
A
The graphs are the same.
B
The graphs are reflected across the x-axis.
C
The graphs are reflected across the y-axis.
37

Which of the following did you include in your response?

A
Sketch the graph of .
Option A
B
Reflect the graph across the y-axis to show the function .
Option B
C
Stretch the graph vertically by a factor of 3 to show the function
Option C
D
Shift the graph up 2 units to show the function
Option D
38

negative infinity to zero0 to infinitynegative infinity to infinity

A
negative infinity to zero
B
0 to infinity
C
negative infinity to infinity
39

2 3

Answers:
The domain of this function is .:negative infinity to infinity
The range of this function is .:3 to infinity

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