The video tutorial explains how to determine if a function has an inverse by using the horizontal line test. It starts with a linear function example, showing that it is a one-to-one function and thus has an inverse. It then examines a parabolic function, demonstrating that it does not have an inverse because it fails the horizontal line test. Additional examples are provided to reinforce the concept. The video concludes by summarizing the criteria for a function to have an inverse: it must be one-to-one and pass the horizontal line test.

What is the purpose of the horizontal line test?

• To determine if a function is continuous

• To check if a function is one-to-one

• To find the slope of a function

• To calculate the derivative of a function

If a function intersects a horizontal line more than once, what can be concluded?

• The function is linear

• The function is quadratic

• The function is one-to-one

• The function does not have an inverse

Why does a parabolic function not have an inverse function?

• It is not continuous

• It fails the horizontal line test

• It has a constant slope

• It is not differentiable

What does the vertical line test determine?

• If a function is decreasing

• If a relation is a function

• If a function is one-to-one

• If a function is increasing

What is a key characteristic of a one-to-one function?

• It passes the vertical line test

• It is always increasing

• It passes the horizontal line test

• It is always decreasing

Which of the following functions is likely to have an inverse?

• A function that passes the horizontal line test

• A function that is not continuous

• A function that fails the vertical line test

• A function that is quadratic

What happens if a function does not pass the horizontal line test?

• It is a one-to-one function

• It does not have an inverse function

• It is a linear function

• It is a continuous function

Tags

CCSS.HSF-BF.B.4D

What is the relationship between one-to-one functions and inverse functions?

• Inverse functions are always one-to-one

• All one-to-one functions have inverse functions

• Only quadratic functions have inverse functions

• One-to-one functions do not have inverse functions

Which test is used to determine if a relation is a function?

• Derivative test

• Slope test

• Vertical line test

• Horizontal line test

What must a function do to have an inverse function?

• Be differentiable

• Be continuous

• Pass the vertical line test

• Pass the horizontal line test