Comparing a Function and Its Inverse

1

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Consider the function. f of x is equal to 3 fourths x plus 12 What is the y -intercept of f inverse of x ?

A

negative 16

B

4 thirds

C

negative 12

D

negative 3 fourths

2

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Consider the function. f of x is equal to 2 and 1 half minus 3 and 1 third x What is the x -intercept of f inverse of x ?

A

open paren 2 and 1 half comma 0 close paren

B

open paren negative 3 tenths comma 0 close paren

C

open paren negative 3 and 1 third comma 0 close paren

D

open paren 3 fourths comma 0 close paren

3

Consider this function. f of x is equal to start absolute value x minus 4 end absolute value plus 6 If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?

A

Since the domain of the original function is limited to x is greater than or equal to 4 , the range of the inverse function is y is less than or equal to 1 .

B

Since the domain of the original function is limited to x is greater than or equal to 6 , the range of the inverse function is y is less than or equal to 6 .

C

Since the range of the original function is limited to y is greater than or equal to 6 , the domain of the inverse function is x is greater than or equal to 6 .

D

Since the range of the original function is limited to y is greater than or equal to 4 , the domain of the inverse function is x is greater than or equal to 1 .

4

Which answer includes a function, its inverse, and a dashed line that verifies the relationship?

A

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line that passes through the origin with a positive slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

B

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line that passes through the origin with a negative slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

C

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line that passes through (0 comma 1) and (6 comma 7) with a positive slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

D

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line that passes through (0 comma 1) and (negative 6 comma 7) with a negative slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

5

Students are asked to graph the inverse, f inverse of x of an absolute value function, f of x after restricting its domain. The directions also ask that the graph include a dashed line that can be used to verify that the functions are inverses of each other. Which student’s work is correct?

A

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma 1) and goes through (6 comma 7). The line (f inverse of x) originates from (0 comma negative 1) and goes through (7 comma 6). A dashed line with a positive slope passes through (0 comma 0) and (7 comma 7).

B

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma negative 1) and goes through (6 comma 7). The line (f inverse of x) originates from (0 comma 1) and goes through (negative 6 comma negative 7). A dashed line with a negative slope passes through (0 comma 0) and (negative 7 comma 7).

C

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma 1) and goes through (6 comma 7). The line (f inverse of x) originates from (1 comma 0) and goes through (7 comma 6). A dashed line with a positive slope passes through (0 comma 0) and (7 comma 7).

D

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two straight lines (f of x) and (f inverse of x), and a dashed line in the first quadrant. The line (f of x) originates from (0 comma 1) and goes through (6 comma 7). The line (f inverse of x) originates from (0 comma 1) and goes through (negative 7 comma negative 6). A dashed line with a negative slope passes through (0 comma 0) and (negative 7 comma 7).

6

In a physics class, the teacher proposes that the velocity of a car in miles per hour and the stopping distance in feet are represented by inverse functions. Assuming this is true, which graph includes a pair of functions for a specific velocity function and the corresponding stopping distance that can be verified as inverses?

A

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has concave up and concave down curves that lie in the first quadrant and intersect each other at (4 comma 4). The concave down curve originates from (0 comma 0) and passes through (2 comma 3). The concave up the curve starts from the origin and goes through (4 comma 4).

B

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves in the first and fourth quadrants, respectively. The curve in the first quadrant starts from the origin and goes through (4 comma 4). The curve in the fourth quadrant originates from (0 comma 0) and passes through (2 comma negative 3).

C

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves in the first and second quadrants, respectively. The curve in the first quadrant starts from the origin, and passes through (4 comma 4). The curve in the second quadrant also originates from the origin, and passes through (negative 6 comma 7).

D

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has concave up and concave down curves that lie in the first quadrant and intersect each other at (4 comma 5). The concave down curve originates from (0 comma 1) and passes through (2 comma 4). The concave curve starts from (0 comma 1) and goes through (4 comma 5).

7

Consider the function and its inverse. f of x is equal to x squared plus 4 and f inverse of x is equal to negative square root of x minus 4 end root When comparing the functions using the equations, which conclusion can be made?

A

The domain of f of x is restricted to x is greater than or equal to 0 , and the domain of f inverse of x is restricted to x is less than or equal to 0 .

B

The domain of f of x is restricted to x is greater than or equal to 0 , and the domain of f inverse of x is restricted to x is greater than or equal to 0 .

C

The domain of f of x is restricted to x is less than or equal to 0 , and the domain of f inverse of x is restricted to x is less than or equal to 4 .

D

The domain of f of x is restricted to x is less than or equal to 0 , and the domain of f inverse of x is restricted to x is greater than or equal to 4 .

8

A linear function and its inverse are given. y is equal to 4 x minus 3 and y is equal to 1 fourth x plus 3 fourths Which tables could be used to verify that the functions are inverses of each other? Choose two correct answers.

A

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 23'; Column 3, 'negative 15'; Column 4, 'negative 3'; Column 5, '1'; Column 6, '13' Row 2: Column 1, 'y'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '1'; Column 6, '4'

B

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 18'; Column 3, 'negative 12'; Column 4, '0'; Column 5, '3'; Column 6, '9' Row 2: Column 1, 'y'; Column 2, 'negative 24'; Column 3, 'negative 18'; Column 4, 'negative 6'; Column 5, 'negative 3'; Column 6, '3'

C

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '1'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, 'negative 23'; Column 3, 'negative 15'; Column 4, 'negative 3'; Column 5, '1'; Column 6, '13'

D

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 24'; Column 3, 'negative 18'; Column 4, 'negative 6'; Column 5, 'negative 3'; Column 6, '3' Row 2: Column 1, 'y'; Column 2, 'negative 18'; Column 3, 'negative 12'; Column 4, '0'; Column 5, '3'; Column 6, '9'

E

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, '1'; Column 3, '3'; Column 4, '5'; Column 5, '7'; Column 6, '9' Row 2: Column 1, 'y'; Column 2, '1'; Column 3, '3'; Column 4, '5'; Column 5, '7'; Column 6, '9'

9

Consider this function. f of x is equal to start absolute value x minus 4 end absolute value plus 6 If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?

A

Since the range of the original function is limited to y is greater than or equal to 4 , the domain of the inverse function is x is greater than or equal to 1 .

B

Since the domain of the original function is limited to x is greater than or equal to 6 , the range of the inverse function is y is less than or equal to 6 .

C

Since the domain of the original function is limited to x is greater than or equal to 4 , the range of the inverse function is y is less than or equal to 1 .

D

Since the range of the original function is limited to y is greater than or equal to 6 , the domain of the inverse function is x is greater than or equal to 6 .

10

Consider the function. f of x is equal to 3 fourths x plus 12 What is the y -intercept of f inverse of x ?

A

negative 16

B

4 thirds

C

negative 3 fourths

D

negative 12

11

Which is an accurate comparison of the functions?

A

The reciprocal of the slope of f of x is the same as the slope of f inverse of x .

B

The opposite of the y - coordinate of the y -intercept of f of x is the same as the x -coordinate of the x -intercept of f inverse of x .

C

The negative reciprocal of the slope of f of x is the same as the slope of f inverse of x .

D

The y - coordinate of the y -intercept of f of x is the same as the y -coordinate of the y -intercept of f inverse of x .

12

When verifying the relationship between the functions using the values in the tables, what conclusion can be made?

A

Since for each ordered pair open paren x comma y close paren for one function there is an ordered pair open paren y comma x close paren for the other function, the functions are not inverses.

B

Since the functions in both tables are increasing, they are not inverses.

C

Since for each ordered pair open paren x comma y close paren for one function there is an ordered pair open paren y comma x close paren for the other function, the functions are inverses.

D

Since the functions in both tables are increasing, they are inverses.

13

Which tables could be used to verify that the functions they represent are inverses of each other? Choose two correct answers.

A

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 120'; Column 3, 'negative 110'; Column 4, 'negative 100'; Column 5, 'negative 95'; Column 6, 'negative 90' Row 2: Column 1, 'y'; Column 2, '2'; Column 3, '27'; Column 4, '27'; Column 5, '227'; Column 6, '627'

B

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 120'; Column 3, 'negative 110'; Column 4, 'negative 100'; Column 5, 'negative 95'; Column 6, 'negative 90' Row 2: Column 1, 'y'; Column 2, '627'; Column 3, '227'; Column 4, '27'; Column 5, '2'; Column 6, '27'

C

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 120'; Column 3, 'negative 110'; Column 4, 'negative 100'; Column 5, 'negative 95'; Column 6, 'negative 90' Row 2: Column 1, 'y'; Column 2, '27'; Column 3, '2'; Column 4, '27'; Column 5, '227'; Column 6, '627'

D

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, '627'; Column 3, '227'; Column 4, '27'; Column 5, '2'; Column 6, '27' Row 2: Column 1, 'y'; Column 2, 'negative 120'; Column 3, 'negative 110'; Column 4, 'negative 100'; Column 5, 'negative 95'; Column 6, 'negative 90'

E

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, '627'; Column 3, '227'; Column 4, '27'; Column 5, '2'; Column 6, '27' Row 2: Column 1, 'y'; Column 2, 'negative 90'; Column 3, 'negative 110'; Column 4, 'negative 100'; Column 5, 'negative 110'; Column 6, 'negative 120'

14

Which statement describes the relationship between the function and its inverse?

A

The range of f of x is y is greater than 0 and the domain of f inverse of x is x is greater than 0 .

B

The range of both f of x and f inverse of x is all real numbers.

C

The domain of f of x is x is greater than 0 and the range of f inverse of x is y is greater than 0 .

D

The domain of both f of x and f inverse of x is all real numbers.

15

In a physics class, the teacher proposes that the velocity of a car in miles per hour and the stopping distance in feet are represented by inverse functions. Assuming this is true, which graph includes a pair of functions for a specific velocity function and the corresponding stopping distance that can be verified as inverses?

A

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has concave up and concave down curves that lie in the first quadrant and intersect each other at (4 comma 4). The concave down curve originates from (0 comma 0) and passes through (2 comma 3). The concave up the curve starts from the origin and goes through (4 comma 4).

B

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves in the first and fourth quadrants, respectively. The curve in the first quadrant starts from the origin and goes through (4 comma 4). The curve in the fourth quadrant originates from (0 comma 0) and passes through (2 comma negative 3).

C

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves in the first and second quadrants, respectively. The curve in the first quadrant starts from the origin, and passes through (4 comma 4). The curve in the second quadrant also originates from the origin, and passes through (negative 6 comma 7).

D

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has concave up and concave down curves that lie in the first quadrant and intersect each other at (4 comma 5). The concave down curve originates from (0 comma 1) and passes through (2 comma 4). The concave curve starts from (0 comma 1) and goes through (4 comma 5).

16

When comparing the functions using the values in the table, which conclusion can be made?

A

The range of f of x includes values such that y is greater than or equal to 1 , so the domain of f inverse of x includes values such that x is greater than or equal to 1 .

B

According to the tables, f of x does not have a y - intercept.

C

According to the tables, f inverse of x does not have an x - intercept.

D

The domain of f of x is restricted such that x is greater than or equal to 0 , so the domain of f inverse of x is restricted such that y is greater than or equal to 0 .

17

Which answer includes a function, its inverse, and a dashed line that verifies the relationship?

A

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line that passes through (0 comma 1) and (negative 6 comma 7) with a negative slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

B

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line that passes through the origin with a negative slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

C

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line that passes through (0 comma 1) and (6 comma 7) with a positive slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

D

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line that passes through the origin with a positive slope. A curve originates from (0 comma 1), goes through (2 comma 3), and then goes up. Another curve starts from (1 comma 0), goes through (3 comma 2), and then goes to the right.

18

Consider the function. f of x is equal to 3 fourths x plus 12 What is the y -intercept of f inverse of x ?

A

negative 3 fourths

B

4 thirds

C

negative 12

D

negative 16

19

Consider the function. f of x is equal to 2 and 1 half minus 3 and 1 third x What is the x -intercept of f inverse of x ?

A

open paren 3 fourths comma 0 close paren

B

open paren 2 and 1 half comma 0 close paren

C

open paren negative 3 tenths comma 0 close paren

D

open paren negative 3 and 1 third comma 0 close paren

20

Consider this function. f of x is equal to start absolute value x minus 4 end absolute value plus 6 If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?

A

Since the domain of the original function is limited to x is greater than or equal to 6 , the range of the inverse function is y is less than or equal to 6 .

B

Since the range of the original function is limited to y is greater than or equal to 6 , the domain of the inverse function is x is greater than or equal to 6 .

C

Since the domain of the original function is limited to x is greater than or equal to 4 , the range of the inverse function is y is less than or equal to 1 .

D

Since the range of the original function is limited to y is greater than or equal to 4 , the domain of the inverse function is x is greater than or equal to 1 .

Comparing a Function and Its Inverse — Quiz Answers

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