Inverse Functions and Their Properties

The video tutorial covers the basics of inverse functions in Algebra 2, including their properties, graphical representation, and algebraic manipulation. It explains how to find inverse functions by switching variables and isolating terms, and discusses the importance of the horizontal line test. The tutorial also introduces one-to-one functions and demonstrates graphing techniques to show symmetry and reflection over the line y = x.

What is the basic idea behind finding an inverse function?

• Switching the variables

• Switching the inputs and outputs

• Switching the domain and range

• Switching the coefficients

What is a key graphical property of inverse functions?

• They intersect the original function at the origin

• They are parallel to the original function

• They are reflections over the line y = x

• They have the same slope as the original function

What does the horizontal line test determine?

• If a function is increasing

• If the inverse of a function is also a function

• If a function is continuous

• If a function is linear

What happens when you compose a function with its inverse?

• You get a constant function

• You get a linear function

• You get a quadratic function

• You get the identity function

How do you find the inverse of a set of ordered pairs?

• Subtract a constant from each pair

• Multiply each pair by a constant

• Switch the x and y values in each pair

• Add a constant to each pair

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

• Add a constant to both sides

• Switch the x and y variables

• Multiply both sides by a constant

• Divide both sides by a constant

Why is the inverse of a parabola not always a function?

• It fails the vertical line test

• It fails the horizontal line test

• It is not differentiable

• It is not continuous

How can you simplify working with fractions when finding inverses?

• Multiply everything by the denominator

• Divide everything by the numerator

• Subtract fractions

• Add fractions together

What does it mean if the original function passes the horizontal line test?

• The inverse is not a function

• The inverse is a function

• The original is not a function

• The original is a one-to-one function

What is a one-to-one function?

• A function that is linear

• A function that is its own inverse

• A function that passes both the vertical and horizontal line tests

• A function that is quadratic