Understanding Functions and Invertibility

The video tutorial explains the concept of functions, focusing on how they map inputs to outputs, and introduces the terms domain and range. It discusses the vertical line test to verify if a graph represents a function and explores the concept of invertibility, explaining how a function can be inverted. The horizontal line test is introduced to determine if a function is invertible. The tutorial concludes by discussing how restricting the domain of a function can make it invertible.

What is the domain of a function?

• The set of all possible inputs

• The set of all possible outputs

• The set of all possible graphs

• The set of all possible equations

What does the vertical line test determine?

• If a graph represents a function

• If a function is invertible

• If a function is differentiable

• If a function is continuous

What is required for a function to be invertible?

• Each input maps to multiple outputs

• Each output maps to multiple inputs

• Each output maps to a unique input

• Each input maps to a unique output

What does the horizontal line test check?

• If a function is continuous

• If a function is invertible

• If a function is differentiable

• If a function is a polynomial

Why is a function not invertible if multiple inputs map to the same output?

• It is not differentiable

• It is not continuous

• It fails the horizontal line test

• It fails the vertical line test

How can a non-invertible function be made invertible?

• By modifying its equation

• By altering its graph

• By restricting its domain

• By changing its range

What happens when you restrict the domain of a function?

• It can pass the horizontal line test

• It becomes non-continuous

• It becomes non-differentiable

• It can pass the vertical line test

What is the result of a function passing the horizontal line test?

• The function is a polynomial

• The function is differentiable

• The function is invertible

• The function is continuous

What is the purpose of restricting a function's domain?

• To make it continuous

• To make it a polynomial

• To make it differentiable

• To make it invertible

What does the summary section emphasize about invertibility?

• It is only applicable to polynomials

• It is always achievable

• It requires domain restriction

• It is not necessary for functions