Exploring Inverse Functions: Graphical and Algebraic Methods

What happens when you interchange the X and Y values in a function?

• The function becomes undefined

• No changes occur to the function

• The domain and range are interchanged

• The function becomes non-linear

How is an inverse function typically denoted?

• 1/f(x)

• f^(-1)(x)

• g(x)

• f(x)^-1

What is the graphical relationship between a function and its inverse?

• Perpendicular bisectors

• Parallel lines

• Overlapping curves

• Reflection over the line y = x

When finding the inverse of a linear function, what is the first step?

• Graph the function

• Solve for y

• Interchange x and y

• Replace f(x) with y

How can you verify if an inverse function is correct?

• Solving for x

• Graphing both functions to see if they are reflections over y = x

• Checking if the domain and range are equal

• By using the horizontal line test

Why might the inverse of a quadratic function not be a function?

• It passes the horizontal line test

• It is always a function

• It fails the vertical line test

• Quadratic functions do not have inverses

What is a key step in finding the inverse of a quadratic function?

• Cubing both sides of the equation

• Taking the square root of both sides

• Adding 2 to both sides

• Multiplying both sides by 2

How can you algebraically determine if two functions are inverses?

• Graphing them on the same axis

• Multiplying them

• Substituting one function into the other

• By adding them together

What result indicates that two functions are inverses of each other?

• The result is 0

• The result is y

• The result is x

• The result is 1

What does it mean if substituting one function into another returns x?

• The functions are identical

• The functions are both quadratic

• The functions are inverses of each other

• The functions are not related