Translations of Exponential Functions

1

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Which equation represents the function f(x) = (1.6)x after it has been translated 5 units up and 9 units to the right?

A

g(x) = (1.6)x + 5 − 9

B

g(x) = (1.6)x + 5 + 9

C

g(x) = (1.6)x − 9 + 5

D

g(x) = (1.6)x + 9 + 5

2

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f(x) = g(x) = – 3

A

The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.

B

The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.

C

The asymptote of g(x) is the asymptote of f(x) shifted three units down.

D

The asymptote of g(x) is the asymptote of f(x) shifted three units up.

3

Which is a stretch of an exponential growth function?

A

f(x) =

B

f(x) =

C

f(x) =

D

f(x) =

4

Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?

A

(2, 12)

B

(2, 18)

C

(2, 7)

D

(3, 7)

5

The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?

A

(–∞, –7)

B

(–∞, –1)

C

(–∞, 1)

D

(–∞, 7)

6

What is the vertex of the graph of f(x) = |x + 3| + 7?

A

(3, 7)

B

(7, 3)

C

(–3, 7)

D

(7, –3)

7

Which describes the range of the parent absolute value function?

A

{y | y is a real number}

B

{y | y is an integer}

C

{y|y > 0}

D

{y|y < 0}

8

Which is the graph of ?

A

Option

B

Option

C

Option

D

Option

9

Which best describes the range of the function f(x) = 2 after it has been reflected over the y-axis?

A

all real numbers

B

all real numbers less than 0

C

all real numbers greater than 0

D

all real numbers less than or equal to 0

10

Which is the initial value that shrinks an exponential growth function by 50%?

A

One-fifth

B

One-fourth

C

One-third

D

One-half

11

Which is the graph of f(x) = 2(3)x?

A

Option

B

Option

C

Option

D

Option

12

Which is the graph of g(x) = – 2?

A

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)

B

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)

C

On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)

D

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)

13

What are the domain and range of f(x) = + 2?

A

domain: ; range: {y | y > 0}

B

domain: ; range: {y | y > 2}

C

domain: {x | x is a real number}; range: {y | y > 2}

D

domain: {x | x is a real number}; range: {y | y > –2}

14

An exponential function f(x) is reflected across the x-axis to create the function g(x). Which is a true statement regarding f(x) and g(x)?

A

The two functions have the same initial value.

B

The two functions will cross each other on the axis.

C

The two functions have reciprocal output values of each other for any given input value.

D

The two functions have opposite output values of each other for any given input value.

15

Which function represents exponential decay?

A

f(x) =

B

f(x) =

C

f(x) = 4

D

f(x) = 4

16

The function f(x) = 8 is reflected across the y-axis to create g(x). Which table of values could be used to graph g(x)?

A

A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entires 128, 32, 8, 2, one-half. The third column is labeled g (x) with entries one-half, 2, 8, 32, 128.

B

A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entires 128, 32, 0, 2, one-half. The third column is labeled g (x) with entries one-half, 2, 0, 32, 128.

C

A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entires 128, 32, 8, 2, one-half. The third column is labeled g (x) with entries negative 128, negative 32, negative 8, negative 2, negative one-half.

D

A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entires 128, 32, 0, 2, one-half. The third column is labeled g (x) with entries negative 128, negative 32, 0, negative 2, negative one-half.

17

Which function represents exponential growth?

A

f(x) = 3x

B

f(x) = x3

C

f(x) = x + 3

D

f(x) = 3x

18

The function f(x) = 5 is reflected over the y-axis. Which equations represent the reflected function? Select two options.

A

f(x) =

B

f(x) =

C

f(x) = 5

D

f(x) = 5(5)x

E

f(x) = 5(5)–x

19

An exponential growth function has an asymptote of y = –3. Which might have occurred in the original function to permit the range to include negative numbers?

A

A whole number constant could have been added to the exponential expression.

B

A whole number constant could have been subtracted from the exponential expression.

C

A whole number constant could have been added to the exponent.

D

A whole number constant could have been subtracted from the exponent.

20

An account is opened with $7,595.96 with a rate of increase of 2% per year. After 1 year, the bank account contains $7,746.90. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years? (Round money values to the nearest penny.)

A

y = 7,746.90(1.02)x

B

y = 7,746.90(0.02)x

C

y = 7,595.96(1.02)x

D

y = 7,595.96(0.02)x

Translations of Exponential Functions — Unit test Answers

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