Functions

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!

Recognizing functions

Not all relationships are functions. In this tutorial, you'll learn which are!

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

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.

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.

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!

Analyzing linear functions

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

Are you bored of the traditional operators of addition, subtraction, multiplication and division? Do even exponents seem a little run-of-the-mill? Well in this tutorial, we will--somewhat arbitrarily--define 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!

Classic function videos

These oldie-but-maybe-goodies 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.

Modeling with one-variable equations and inequalities

Now that you know how to solve linear, quadratic and exponential equations, we'll apply these incredible skills to a wide-range of real-world (and sometimes not-so-real-world) situations.