# Algebra II

Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
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# Functions and their graphs

Revisiting what a function is and how we can define and visualize one.
All content in “Functions and their graphs”

## 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!

## Function expressions

We'll now see what it means to add, subtract, multiply and divide functions!

## 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.

## Recognizing functions

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

## 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.

## Piecewise functions

In this tutorial, we will get practice looking at wackier functions that are defined interval by interval (or piece by piece)!

## Properties and features of functions

You know a function when you see one, but are curious to start looking deeper at their properties. Some functions seem to be mirror images around the y-axis while others seems to be flipped mirror images while others are neither. How can we shift and reflect them? This tutorial addresses these questions by covering even and odd functions. It also covers how we can shift and reflect them. Enjoy!

## Comparing and interpreting functions

In this tutorial, we'll dive deeper into actually thinking about what functions represent and how one function compares to another.

## Undefined and indeterminate answers

In second grade you may have raised your hand in class and asked what you get when you divide by zero. The answer was probably "it's not defined." In this tutorial we'll explore what that (and "indeterminate") means and why the math world has left this gap in arithmetic. (They could define something divided by 0 as 7 or 9 or 119.57 but have decided not to.)

## More mathy functions

In this tutorial, we'll start to use and define functions in more "mathy" or formal ways.