Understanding Inverses of Quadratic Functions

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

• Graph the function

• Replace y with f(x)

• Switch x and y

• Solve for x

Why is the inverse of a quadratic function not a function?

• It is not continuous

• It is multi-valued

• It does not have a domain

• It is not differentiable

What is the relationship between the domain of a function and the range of its inverse?

• They are unrelated

• The domain of the inverse is the range of the function

• They are equal

• The domain of the function is the range of the inverse

What is the purpose of restricting the domain of a quadratic function?

• To make the inverse a function

• To simplify the graph

• To increase the range

• To eliminate complex numbers

How do you determine where to restrict the domain of a quadratic function?

• By finding the axis of symmetry

• By finding the x-intercept

• By finding the vertex

• By finding the y-intercept

In the practical example, what is the vertex used for domain restriction?

• (2, 3)

• (1, 2)

• (0, 0)

• (-3, -1)

What is the range of the inverse function after domain restriction in the example?

• Negative 3 to infinity

• Negative infinity to 3

• 1 to infinity

• 3 to infinity

What is the significance of the line y = x in relation to inverses?

• It is the line of reflection

• It is the axis of symmetry

• It is the tangent line

• It is the line of best fit

What happens to the graph of the inverse when the domain is restricted?

• It disappears

• It becomes a complete reflection over y = x

• It becomes a vertical line

• It becomes a horizontal line

What is the domain of the inverse function in the practical example?

• 2 to infinity

• Negative infinity to 1

• 1 to infinity

• Negative 1 to infinity