Exploring Inverse Relations and Functions

The video tutorial covers inverse relations and functions, explaining how to determine if an inverse is a function using vertical and horizontal line tests. It provides algebraic methods to find inverse functions and discusses the inverse reflection principle for graphical representation. The inverse composition rule is introduced to verify inverses, and examples are provided, including finding the inverse of a square root function.

What does it mean for two ordered pairs to be in an inverse relation?

• Their values are identical.

• Their values are doubled.

• Their values are swapped.

• Their values are squared.

What test is used to determine if an inverse is a function?

• Diagonal line test

• Vertical line test

• Circular line test

• Horizontal line test

What does the vertical line test check for?

• If a graph represents a function

• If a graph represents an inverse function

• If a graph passes the horizontal line test

• If a graph is symmetric

What does the horizontal line test determine?

• If a function is quadratic

• If a function is increasing

• If a function is one-to-one

• If a function is decreasing

When finding an inverse function algebraically, what is the first step?

• Solve for y.

• Check if the function is one-to-one.

• State the domain restrictions.

• Switch x and y in the equation.

What is necessary for a function to have an inverse function?

• It must be a linear function.

• It must pass the vertical line test.

• It must be a polynomial function.

• It must pass the horizontal line test.

What does switching x and y in an equation accomplish when finding an inverse function?

• It determines the function's domain.

• It finds the inverse function.

• It simplifies the equation.

• It helps solve for y.

What principle helps us understand inverse functions graphically?

• Inverse reflection principle

• Inverse square principle

• Inverse operation principle

• Inverse proportionality principle

How can you verify two functions are inverses of each other?

• By subtracting one from the other

• By using the inverse composition rule

• By dividing one by the other

• By adding them together

What is the result of applying the inverse composition rule correctly?

• You get a fraction.

• You get a square root.

• You get x.

• You get 0.