Khan Academy on a Stick
Functions
Identifying, solving, and graphing various types of functions.
 What is a function

Difference between Equations and Functions
Jesse Roe and Sal talk about the difference between equations and functions

Function example problems
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Linear Function Graphs

Ex: Constructing a function
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Basic Linear Function

Understanding Function Notation Example 1)
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Understanding Function Notation Example 2)
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 Understanding Function Notation Example 3)

Testing if a relationship is a function
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Testing if a relationship is a function

Graphical Relations and Functions
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Graphical Relations and Functions

Functions as Graphs
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 Recognizing functions (example 1)

Recognizing functions (example 2)
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Relations and Functions
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Relations and Functions

Functional Relationships 1
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Functional Relationships 1

Recognizing functions (example 3)
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 Recognizing functions (example 4)
 Recognizing functions (example 5)
Function introduction
Relationships can be any association between sets of numbers while functions have only one output for a given input. This tutorial works through a bunch of examples of testing whether something is a valid function. As always, we really encourage you to pause the videos and try the problems before Sal does!

Domain of a function
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Figuring out the domain of a function

Domain and Range of a Relation
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Domain and Range of a Relation

Domain and Range of a Function Given a Formula
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Domain and Range of a Function Given a Formula

Domain and Range 1
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Domain and Range 1

Domain of a Radical Function
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Domain of a Radical Function

Domain and Range 2
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Domain and Range 2

Domain and Range of a Function
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Domain and range
What values can you and can you not input into a function? What values can the function output? The domain is the set of values that the function is defined for (i.e., the values that you can input into a function). The range is the set of values that the function output can take on. This tutorial covers the ideas of domain and range through multiple worked examples. These are really important ideas as you study higher mathematics.

Direct and Inverse Variation
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Understanding direct and inverse variation

Recognizing Direct and Inverse Variation
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Examples of variables varying directly and inversely

Proportionality Constant for Direct Variation
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Proportionality Constant for Direct Variation

Direct Variation Models
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Direct Variation Models

Direct Variation 1
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Direct Variation 1

Inverse Variation Application
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Inverse Variation Application

Direct Inverse and Joint Variation
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Direct Inverse and Joint Variation

Direct Variation Application
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Direct Variation Application
Direct and inverse variation
Whether you are talking about how force relates to acceleration or how the cost of movie tickets relates to the number of people going, it is not uncommon in this universe for things to vary directly. Similarly, when you are, say, talking about how hunger might relate to seeing roadkill, things can vary inversely. This tutorial digs deeper into these ideas with a bunch of examples of direct and inverse variation.

Ex 1: Evaluating a function
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Evaluating Functions

Ex 2: Graphing a basic function
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Graphing a Basic Function

Graphing a parabola with a table of values
Graphing a parabola with a table of values

Ex 4: Graphing radical functions
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Graphing Radical Functions

Ex: Graphing exponential functions
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Graphing Exponential Functions
Graphing functions
You've already graphed functions when you graphed lines and curves in other topics so this really isn't anything new. Now we'll do a few more examples in this tutorial, but we'll use the function notation to make things a bit more explicit.

Quotient of Functions
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Quotient of functions and factoring by grouping

Sum of Functions
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Sum of Functions

Product of Functions
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Product of Functions

Difference of Functions
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Difference of Functions

Evaluating a function expression
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 Evaluating composite functions example
Evaluating function expressions
This is a super fun tutorial where we'll evaluate expressions that involve functions. We'll add, subtract, multiply and divide them. We'll also do composite functions which involves taking the output of one function to be the input of another one! As always, pause the video and try the problem before Sal does!

Introduction to Function Inverses
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Introduction to Function Inverses

Function Inverse Example 1
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Function Inverse Example 1

Function Inverses Example 2
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Function Inverses Example 2

Function Inverses Example 3
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Function Inverses Example 3
Function inverses
Functions associate a set of inputs with a set of outputs (in fancy language, they "map" one set to another). But can we go the other way around? Are there functions that can start with the outputs as inputs and produce the original inputs as outputs? Yes, there are! They are called function inverses! This tutorial works through a bunch of examples to get you familiar with the world of function inverses.

New operator definitions
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Getting comfortable with evaluating newly defined function operators

New operator definitions 2
Worked examples of working with newly defined operators
New operator definitions
Are you bored of the traditional operators of addition, subtraction, multiplication and division? Do even exponents seem a little runofthemill? Well in this tutorial, we willsomewhat arbitrarilydefine completely new operators and notation (which are essentially new function definitions without the function notation). Not only will this tutorial expand your mind, it could be the basis of a lot of fun at your next dinner party!

Introduction to functions
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An introduction to functions.

Functions Part 2
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More examples of solving function problems

Functions (Part III)
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Even more examples of function exercises. Introduction of a graph as definition of a function.

Functions (part 4)
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An example of a functions problem submitted by a youtube viewer
Classic function videos
These oldiebutmaybegoodies are the original function videos that Sal made years ago for his cousins. Despite the messy handwriting, some people claim that they like these better than the new ones (they claim that there is a certain charm to them). We'll let you decide.