Exponential Functions — Test Answers

1

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What is the initial value of the exponential function shown on the graph?

A

1

B

0

C

4

D

2

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Which function represents g of x , a reflection of f of x is equal to 1 half times 3 to the x th power across the y -axis?

A

g of x is equal to 1 half times 3 raised to the negative x power

B

g of x is equal to 2 times 3 to the x th power

C

g of x is equal to 2 times 3 raised to the negative x power

D

g of x is equal to negative 1 half times 3 to the x th power

3

Which function represents a reflection of f of x is equal to 5 times 0 point 8 to the x th power across the x -axis?

A

g of x is equal to 5 times 0 point 8 raised to the negative x power

B

g of x is equal to negative 5 times 0 point 8 to the x th power

C

g of x is equal to 5 times negative 0 point 8 to the x th power

D

g of x is equal to 1 fifth times 0 point 8 to the x th power

4

What is the value of k ?

A

negative 3

B

3

C

5

D

negative 5

5

Which exponential function is represented by the graph?

A

f of x is equal to 2 times 1 half to the x th power

B

f of x is equal to 1 half times 2 to the x th power

C

f of x is equal to 2 times 2 to the x th power

D

f of x is equal to 1 half times 1 half to the x th power

6

What is the range of f of x is equal to 3 fourths to the x th power minus 4 ?

A

start set y such that y is less than negative 4 end set

B

start set y such that y is greater than negative 4 end set

C

start set y such that y is less than 3 fourths end set

D

start set y such that y is greater than 3 fourths end set

7

The curve through the ordered pairs 0 comma 10 , 1 comma 5 , and 2 comma 2 point 5 can be represented by the function f of x is equal to 10 times 0 point 5 to the x th power What is the multiplicative rate of change of the function?

A

0 point 5

B

2

C

5

D

2 point 5

8

Which equation represents an exponential function with an initial value of 500 ?

A

f of x is equal to 100 times x to the 5th power

B

f of x is equal to 500 times 2 to the x th power

C

f of x is equal to 500 times x squared

D

f of x is equal to 100 times 5 to the x th power

9

The graph of g of x is the result of translating the graph of f of x is equal to 3 to the x th power six units to the right. What is the equation of g of x ?

A

g of x is equal to 3 to the x th power plus 6

B

g of x is equal to 3 raised to the x minus 6 power

C

g of x is equal to 3 to the x th power minus 6

D

g of x is equal to 3 raised to the x plus 6 power

10

Which is a stretch of an exponential decay function?

A

f of x is equal to 4 fifths times 4 fifths to the x th power

B

f of x is equal to 4 fifths times 5 fourths to the x th power

C

f of x is equal to 5 fourths times 5 fourths to the x th power

D

f of x is equal to 5 fourths times 4 fifths to the x th power

11

Which is equivalent to 216 raised to the 1 third power ?

A

36

B

72

C

3

D

6

12

Which is the graph of f of x is equal to 4 times 1 half to the x th power ?

A

Image with description A coordinate plane displays the x-axis labeled from negative 3 to 7 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1. A decreasing curve passes through approximately the points 0 comma 2, 1 comma 1.3, 2 comma 1, and 6 comma 0.3.

B

Image with description A coordinate plane displays the x-axis labeled from negative 3 to 7 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1. A decreasing curve passes through approximately the points 0 comma 4, 1 comma 2, 2 comma 1, and 4 comma 0.25.

C

Image with description A coordinate plane displays the x-axis labeled from negative 3 to 7 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1. A decreasing curve passes through approximately the points 0 comma 4, 1 comma 2, 2 comma 1, and 3 comma 0.5.

D

Image with description A coordinate plane displays the x-axis labeled from negative 3 to 7 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1. A decreasing curve passes through approximately the points 0 comma 2, 1 comma 0.7, 2 comma 0.25, and 4 comma 0.05.

13

The function f of x is equal to 2 times 5 to the x th power can be used to represent the curve through the points 1 comma 10 , 2 comma 50 , and 3 comma 250 What is the multiplicative rate of change of the function?

A

5

B

10

C

32

D

2

14

When simplified, the expression open paren x raised to the 1 eighth power close paren times open paren x raised to the 3 eighths power close paren is 12 Which is a possible value of x ?

A

6

B

256

C

144

D

24

15

Which is the graph of f of x is equal to 1 fourth times 4 to the x th power ?

A

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 with an increment of 1 and y axis is ranges from negative 6 to 6 with increment of 1. An exponential function approaches y equal to 0 in quadrant I. The curves up to the left and passes through points 0 comma 4 and 1 comma 1. The arrow is present on both ends of curve.

B

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 with an increment of 1 and y axis is ranges from negative 6 to 6 with increment of 1. An exponential function approaches y equal to 0 in quadrant II and passes through points 3 comma 2 and 4 comma 4. The arrow is present on both ends of curve.

C

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 with an increment of 1 and y axis is ranges from negative 6 to 6 with increment of 1. An exponential function approaches y equal to 0 in quadrant I. The curves up to the left and passes through points 2 comma 1 and 0 comma 4. The arrow is present on both ends of curve.

D

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 with an increment of 1 and y axis is ranges from negative 6 to 6 with increment of 1. An exponential function approaches y equal to 0 in quadrant II and passes through points 1 comma 1 and 2 comma 4. The arrow is present on both ends of curve.

16

The function f of x is defined as f of x is equal to 1 third times 6 to the x th power Which table of values could be used to graph g of x , a reflection of f of x across the x -axis?

A

Table with 3 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'f of x'; Column 3, 'g of x' Row 2: Column 1, 'negative 2'; Column 2, '1 over 108'; Column 3, 'negative 1 over 108' Row 3: Column 1, 'negative 1'; Column 2, '1 over 18'; Column 3, 'negative 1 over 18' Row 4: Column 1, '0'; Column 2, '1 third'; Column 3, 'negative 1 third' Row 5: Column 1, '1'; Column 2, '2'; Column 3, 'negative 2' Row 6: Column 1, '2'; Column 2, '12'; Column 3, 'negative 12'

B

Table with 3 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'f of x'; Column 3, 'g of x' Row 2: Column 1, 'negative 2'; Column 2, '1 over 108'; Column 3, 'negative 1 over 108' Row 3: Column 1, 'negative 1'; Column 2, '1 over 18'; Column 3, 'negative 1 over 18' Row 4: Column 1, '0'; Column 2, '0'; Column 3, '0' Row 5: Column 1, '1'; Column 2, '2'; Column 3, 'negative 2' Row 6: Column 1, '2'; Column 2, '12'; Column 3, 'negative 12'

C

Table with 3 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'f of x'; Column 3, 'g of x' Row 2: Column 1, 'negative 2'; Column 2, '1 over 108'; Column 3, '12' Row 3: Column 1, 'negative 1'; Column 2, '1 over 18'; Column 3, '2' Row 4: Column 1, '0'; Column 2, '1 third'; Column 3, '1 third' Row 5: Column 1, '1'; Column 2, '2'; Column 3, '1 over 18' Row 6: Column 1, '2'; Column 2, '12'; Column 3, '1 over 108'

D

Table with 3 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'f of x'; Column 3, 'g of x' Row 2: Column 1, 'negative 2'; Column 2, '1 over 108'; Column 3, '12' Row 3: Column 1, 'negative 1'; Column 2, '1 over 18'; Column 3, '2' Row 4: Column 1, '0'; Column 2, '0'; Column 3, '0' Row 5: Column 1, '1'; Column 2, '2'; Column 3, '1 over 18' Row 6: Column 1, '2'; Column 2, '12'; Column 3, '1 over 108'

17

Which best describes the range of the function f of x is equal to 2 thirds times 6 to the x th power after it has been reflected over the x -axis?

A

all real numbers greater than 0

B

all real numbers less than 0

C

all real numbers

D

all real numbers less than or equal to 0

18

What is the simplified value of the exponential expression 16 raised to the 1 fourth power ?

A

4

B

1 fourth

C

1 half

D

2

19

Which is equivalent to 256 raised to the 3 fourths power ?

A

192

B

64

C

4

D

12

20

Which table represents exponential growth?

A

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '4' Row 4: Column 1, '3'; Column 2, '6' Row 5: Column 1, '4'; Column 2, '8'

B

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '4' Row 4: Column 1, '3'; Column 2, '6' Row 5: Column 1, '4'; Column 2, '10'

C

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '4' Row 4: Column 1, '3'; Column 2, '8' Row 5: Column 1, '4'; Column 2, '16'

D

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '4' Row 4: Column 1, '3'; Column 2, '7' Row 5: Column 1, '4'; Column 2, '11'

Exponential Functions — Test Answers

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