One-to-One Functions and Inverses

This video tutorial explains inverse functions, focusing on the necessity for a function to be one-to-one to have an inverse. It introduces the horizontal line test as a method to determine if a function is one-to-one. The video provides examples of functions that are and are not one-to-one, and uses a graphical approach to illustrate the concept of reflection across the line y=x. It also demonstrates how to manipulate a function to make it one-to-one, ensuring it has an inverse. The tutorial concludes with a summary of the key points discussed.

What is the primary requirement for a function to have an inverse?

• It must be one-to-one.

• It must be periodic.

• It must be continuous.

• It must be differentiable.

What test is used to determine if a function is one-to-one?

• Derivative test

• Horizontal line test

• Slope test

• Vertical line test

If a horizontal line intersects a graph more than once, what does it indicate?

• The function is quadratic.

• The function is linear.

• The function is not one-to-one.

• The function is one-to-one.

What does the reflection of a function across the line y = x represent?

• The derivative of the function

• The tangent to the function

• The inverse of the function

• The integral of the function

What happens to the inverse if the original function is not one-to-one?

• The inverse will be quadratic.

• The inverse will be linear.

• The inverse will not be a function.

• The inverse will be a function.

How can a function be manipulated to become one-to-one?

• By making it periodic

• By adjusting points to pass the horizontal line test

• By making it continuous

• By increasing its slope

What test does the inverse of a function need to pass to be considered a function?

• Vertical line test

• Horizontal line test

• Derivative test

• Slope test

What is the result if a horizontal line intersects a graph in three points?

• The function is one-to-one.

• The function is linear.

• The function is quadratic.

• The function is not one-to-one.

What is the significance of the dashed curve in the graphical representation?

• It represents the derivative of the function.

• It represents the inverse function.

• It represents the integral of the function.

• It represents the original function.

What is the main takeaway regarding the horizontal and vertical line tests?

• They only apply to linear functions.

• They are used to find the slope of a function.

• They are essential for determining if a function and its inverse are valid.

• They are not related to inverse functions.