Exploring Inverse Functions and Their Graphs

What is the first step in finding the inverse of a function?

• Replace f(x) with y

• Switch x and y in the equation

• Graph the function

• Solve for x

What is the inverse function of f(x) = 3x + 9?

• x = 3y + 9

• y = (x - 9) / 3

• y = 3x - 9

• x = (y - 9) / 3

How do you find the inverse of a quadratic function?

• By subtracting 4 from both sides

• By squaring both sides

• By taking the square root of both sides

• By adding 4 to both sides

What must be added when taking the square root of both sides?

• Nothing

• + and - signs

• A constant

• The variable x

What is the inverse function of f(x) = x^3 + 8?

• y = 3√(x - 8)

• y = (x - 8)^3

• y = 3√(x + 8)

• y = (x - 8) / 3

What is the inverse function of f(x) = the cube root of 3x + 8?

• y = 3x^3 + 8

• y = (x - 8)^3

• y = (x^3 - 8) / 3

• y = 3√(x + 8)

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

• By solving for x

• By switching x and y

• By graphing them

• By performing function composition

What does the horizontal line test determine?

• If a function has an inverse

• If a function is increasing

• If a function is one-to-one

• If a function is quadratic

What property do inverse functions have on a graph?

• They are symmetric about the line y = x

• They are symmetric about the y-axis

• They have the same slope

• They intersect at the origin

If a function fails the horizontal line test, what does it imply about its inverse?

• The inverse is also a function

• The inverse fails the vertical line test

• The inverse passes the vertical line test

• The inverse is a linear function