Quiz about Inverse Functions Graphically

Question 1

A graph and its inverse are always symmetrical about the line...

Accepted Answer

$$y=x$$

Answer

$$y=-x$$

Answer

$$y=0$$

Answer

$$y=1$$

Question 2

To graph the inverse of a function...

Accepted Answer

Switch the x and y coordinates and plot the new points

Answer

Rotate it around the origin

Answer

Reflect it across the x-axis

Answer

Reflect it across the y-axis

Question 3

The graph shows the inverse, g(x) is a reflection of f(x) with respect to what line?

Accepted Answer

The line $$y=x$$

Answer

The line $$y=1$$

Answer

The y-axis

Answer

The x-axis

Question 4

Are these the graphs of two inverse functions?

Accepted Answer

Yes

Answer

No

Answer

No way to tell

Question 5

Are these functions inverses?

Accepted Answer

Yes

Answer

No

Question 6

What's the best description?

Accepted Answer

They are inverse functions.

Answer

They are both functions, but not inverse functions.

Answer

They are reflected over y=x, but they are not both functions.

Answer

They are not reflected over y=x, and they are not both functions.

Question 7

What is the best description of f(x) in red and g(x) in green?

Accepted Answer

They are inverse functions because they both are functions and they are reflections of each other over y = x.

Answer

They are both functions, but not inverse functions.

Answer

They are reflected over y=x, but they are not both functions.

Answer

They are not reflected over y=x, and they are not both functions.

Question 8

Are these functions inverses?

Accepted Answer

Yes

Answer

No

Question 9

How could you find the inverse of f(x) graphically? **choose the TWO correct answers**

Accepted Answer

Reflect points of f(x) across the line y = x

Accepted Answer

Swap x and y coordinates for each point of f(x)

Answer

Reflect points of f(x) across the line y = -x

Answer

Reflect points of f(x) across the line y = 0

Question 10

The equation of f(x) goes through the points (1, 4) and (4, 6).

What points does the inverse go through?

Accepted Answer

(4, 1) and (6, 4)

Answer

(1, 4) and (4, 6)

Answer

(-4, -1) and (-6, -4)

Answer

(-1, -4) and (-4, -6)

Question 11

Are these inverse functions?

Accepted Answer

yes

Answer

no

Question 12

What is the process of finding inverse functions graphically?

Accepted Answer

Reflecting the points of the original function across the line y = x.

Answer

Reflecting the points of the original function across the line y = -x.

Answer

Rotating the points of the original function 90 degrees counterclockwise.

Answer

Finding the points of intersection between the original function and the line y = x.

Question 13

What is the relationship between a linear function and its inverse in terms of their graphs?

Accepted Answer

They are reflections of each other across the line y = x.

Answer

They are parallel to each other.

Answer

They intersect at the origin.

Answer

They have the same slope.

Question 14

What is the purpose of using the Horizontal Line Test?

Accepted Answer

To determine if a function is one-to-one or not.

Answer

To determine if a function is linear or not.

Answer

To determine if a function is continuous or not.

Answer

To determine if a function is increasing or decreasing.

Question 15

If a linear function passes the Horizontal Line Test, does it have an inverse? (True/False)

Accepted Answer

True

Answer

Not enough information

Answer

Sometimes

Answer

False

Question 16

Can a linear function and its inverse have the same graph? (True/False)

Accepted Answer

False

Answer

Not sure

Answer

Sometimes

Answer

True

Question 17

How can you define the inverse function using ordered pairs?

Accepted Answer

Swap the x and y values of each ordered pair.

Answer

Divide the x and y values of each ordered pair.

Answer

Multiply the x and y values of each ordered pair.

Answer

Add the x and y values of each ordered pair.

Question 18

If a linear function has a vertical line passing through more than one point on its graph, does it have an inverse? (True/False)

Accepted Answer

False

Answer

Sometimes

Answer

True

Answer

Not enough information

Inverse Functions Graphically

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