Understanding Inverse Functions

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

• They are identical.

• They intersect at the origin.

• They are symmetric about the line Y = X.

• They are parallel to each other.

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

• Multiply the function by 2.

• Exchange the X and Y variables.

• Add 5 to the function.

• Subtract 3 from the function.

What happens to the signs of the terms when dividing by negative one?

• They become positive.

• They change to the opposite sign.

• They remain the same.

• They double.

Why do we use only the principal root when finding the inverse of a function?

• To make the calculation easier.

• To simplify the graph.

• To avoid negative numbers.

• To ensure the result is a function.

What operation is used to eliminate the square in the equation when finding the inverse?

• Square root

• Subtraction

• Addition

• Multiplication

What does the vertical line test determine?

• If a graph is quadratic.

• If a graph is a function.

• If a graph is symmetric.

• If a graph is linear.

What is the result when composing a function with its inverse?

• 1

• 0

• X

• Y

What is the final form of the inverse function in this example?

• A square root function

• A quadratic function

• An exponential function

• A linear function

What is the purpose of graphing the function and its inverse together?

• To check for symmetry about the line Y = X.

• To calculate the area under the curve.

• To find the intersection points.

• To determine the slope.

What is the significance of the line Y = X in the context of inverse functions?

• It is the horizontal asymptote.

• It is the vertical asymptote.

• It is the axis of symmetry.

• It is the line of best fit.