One to one functions

One to one functions

Basic concepts: Inverse functions,

Lessons

\bullet To determine if an expression is a function, we perform the vertical line test.

\bullet Surjective/Onto: For every yy value, there exists at least one xx value.

\bullet Injective/Into/one-to-one: For every yy value, there exists at most one xx value.

\bullet To determine if a function is one-to-one, we perform the horizontal line test.

  • Introduction
    Introduction to one to one functions

    i. Review: How are functions, Surjective functions and Injective functions related?

    ii. How to determine if an expression is a function?

    iii. What are Surjective functions?

    iv. What are one to one functions?


  • 1.
    Discussing the Differences Between Surjective and Injective Functions

    Identify the differences between Surjective and Injective functions and give an example for each of the functions.


  • 2.
    Identifying One-to-One Functions On a Graph

    Learning the Horizontal Line Test and understanding how it can be implemented to identify one-to-one functions on a graph.


  • 3.
    Applying the Horizontal Line Test

    Determine if the following graphs are one-to-one functions using the horizontal line test.

    i. Determine if the graph is an one to one function 1.

    ii. Determine if the graph is an one to one function 2

    iii. Determine if the graph is an one to one function 3

    iv. Determine if the graph is an one to one function 4