Inverse Functions and Their Properties

This lesson covers function transformations, focusing on inverse relations. It explains the vertical and horizontal line tests to determine if a graph represents a function or its inverse. The lesson includes graphing techniques for inverse functions, understanding domain and range, and provides examples and exercises to reinforce learning. Key ideas are recapped at the end.

What is the main focus of the lesson on function transformations?

• Understanding the concept of limits

• Sketching the graph of the inverse of a relation

• Learning about polynomial functions

• Exploring trigonometric identities

What does the vertical line test determine?

• If a graph is a circle

• If a graph is a parabola

• If a graph is a straight line

• If a graph represents a function

How do you sketch the graph of the inverse of a function?

• By translating the graph upwards

• By reflecting the graph over the x-axis

• By switching the x and y coordinates

• By rotating the graph 90 degrees

What is the first step in finding the equation of an inverse function?

• Multiply all terms by 2

• Switch x and y in the equation

• Add 5 to the equation

• Divide by the coefficient of x

What happens to the domain and range when finding the inverse of a function?

• They remain unchanged

• They are divided by 2

• They are multiplied by 2

• They are switched

What does the horizontal line test determine?

• If the inverse of a graph is a function

• If a graph is symmetric

• If a graph is linear

• If a graph is a function

In the example of sketching an inverse graph, what is determined about the inverse?

• It is always a function

• It may not be a function

• It is never a function

• It is always linear

How does the domain of the original function relate to the inverse?

• It becomes the range of the inverse

• It remains the same

• It is doubled

• It is halved

Which graph represents a function and its inverse correctly?

• Graph D

• Graph C

• Graph B

• Graph A

What is the equation of the inverse of y = 1/2x - 2/3?

• y = -2x + 4

• y = 2x + 4/3

• y = 3x - 1/2

• y = 6x + 4/3