Worksheet on Transformations of Exponential Functions

Multiple Choice
Identify the choice that best completes the statement or answers the question.

____ 1. Which of the following functions represents after a reflection on the x-axis and a vertical translation
5 units down?
a. c.

b. d.

____ 2. What is the equation of the asymptote for the function ?

a. y = 3 c. x = 3
b. y = –3 d. y = 4

____ 3. Consider the function . Which of the following graphs represents the base function as a
dotted curve and the transformations applied to the base function as a solid curve?
a. y
c. y

5 7

4 6

3 5

2 4

1 3

2
–5 –4 –3 –2 –1 1 2 3 4 5 x
–1 1

–2
–5 –4 –3 –2 –1 1 2 3 4 5 x
–3 –1

–4 –2

–5 –3

b. y
d. y

7 7

6 6

5 5

4 4

3 3

2 2

1 1

–5 –4 –3 –2 –1 1 2 3 4 5 x –5 –4 –3 –2 –1 1 2 3 4 5 x
–1 –1

–2 –2

–3 –3
____ 4. Which of the following functions represents after a vertical compression by the factor and a reflec-
tion on the y-axis?
a. c.

b. d.

____ 5. The graph shown represents a transformation of the function . What is the equation for the transform-
ation?
y

–8 –7 –6 –5 –4 –3 –2 –1 1 2 x
–1

–2

–3

–4

–5

–6

–7

a. c.

b. d.

Short Answer

6. Use transformations to sketch the function . State the domain and range.

7. Compare and contrast the functions and .

8. The function is the result of transformations of . Describe the sequence of
transformations.
Worksheet on Transformations of Exponential Functions
Answer Section

MULTIPLE CHOICE

1. ANS: C PTS: 1 REF: Knowledge and Understanding

OBJ: 4.6 - Transformations of Exponential Functions
2. ANS: A PTS: 1 REF: Knowledge and Understanding
OBJ: 4.6 - Transformations of Exponential Functions
3. ANS: D PTS: 1 REF: Knowledge and Understanding
OBJ: 4.6 - Transformations of Exponential Functions
4. ANS: A PTS: 1 REF: Knowledge and Understanding
OBJ: 4.6 - Transformations of Exponential Functions
5. ANS: D PTS: 1 REF: Knowledge and Understanding
OBJ: 4.6 - Transformations of Exponential Functions

SHORT ANSWER

6. ANS:
y

–12 –10 –8 –6 –4 –2 2 4 6 8 x
–2

–4

–6

–8

–10

–12

–14

Domain = {x R}
Range = {y R | y < –1}

PTS: 1 REF: Knowledge and Understanding

OBJ: 4.6 - Transformations of Exponential Functions
7. ANS:
Both functions are the same. Eight is a power of 2, so, to make it easier to compare with , I substituted
for 8 in the first equation.
 PTS: 1 REF: Communication
OBJ: 4.6 - Transformations of Exponential Functions
8. ANS:
There is a vertical stretch by a factor of 2 and a reflection in the x-axis. There is a horizontal compression by a

factor of . There is a translation 3 units to the right and 9 units up.

PTS: 1 REF: Communication

OBJ: 4.6 - Transformations of Exponential Functions