How does the graph of a function compare to it's inverse

The video tutorial explains the concept of functions and their inverses, using F(x) = x + 2 and its inverse F⁻¹(x) = x - 2 as examples. It demonstrates how to graph these functions on the same axes and discusses the special case where the function and its inverse are parallel lines. The tutorial emphasizes that inverses are reflections over the line y = x and explains how to find an inverse by swapping the x and y coordinates of a function's points. An example is provided to illustrate this process.

What is the inverse of the function f(x) = x + 2?

• f⁻¹(x) = x + 2

• f⁻¹(x) = x - 2

• f⁻¹(x) = x / 2

• f⁻¹(x) = 2x + 1

Which line do inverse functions reflect over?

• y = 2x

• y = x

• y = 0

• x = 0

What is a key characteristic of inverse functions?

• They are reflections over the line y = x.

• They intersect at the origin.

• They are always parallel.

• They have the same slope.

How do you find the inverse of a function using its points?

• Swap the x and y coordinates.

• Multiply each coordinate by 2.

• Subtract 2 from each coordinate.

• Add 2 to each coordinate.

If a point on f(x) is (0, 2), what is the corresponding point on f⁻¹(x)?

• (2, 0)

• (0, -2)

• (0, 2)

• (-2, 0)