After a certain point in Algebra 2, everything in every math class you'll see is going to be functions. Why are they called functions? Not sure. Since f(x) basically just means "y", they could have just stuck with that and everyone would have been a lot happier. Oh well! Turns out they're not that bad, though, if you just remember that "f(x) is really y" thing. In this chapter we'll introduce the concepts of domain, range, x-intercepts, y-intercepts, and graphing functions, but all those things will be covered in much more depth in later chapters, where we'll have a chapter for each type of function. This chapter is a great place to start, though, if you're confused about what these terms mean, and I'll show you a simple four-step process for finding inverse functions.
Intro to Functions
In this video we'll introduce lots of concepts of functions, such as: what "f(x)" means, function notation, the vertical line test, "one-to-one" functions, how to plug numbers into a function, and even those silly problems where they give you a bunch of points and ask if they're a function.
Graphing Functions By Plugging In
There are lots of fancy ways to graph functions, and we'll get into that in other videos. But the fall-back method you'll be happy to have in your back pocket is "plugging s*@#! in. (That was "stuff", what did you think I meant?)"
Domain & Range
The domain of a function is all it's x-values, usually an interval. Range is the set of y-values. In this video I cover how to find domain and range using the two big rules you never want to break: dividing by zero, and square rooting a negative. Don't do it!
Like the similarly-named sketches which assist the police in tracking down suspects, these combinations of various functions will "arrest" you in a fit of confusion as you ponder the domain of g(f(x)). (Pun very much intended. You're welcome!)
Believe it or not, you've been using inverse functions since you solved your first algebra equation. (Multiplication is the inverse of division, addition is the opposite of subtraction.) In this long video we'll get into a step-by-step process to find inverse functions, graph inverse functions, and anticipate and assess their function-hood.
Finding X and Y Intercepts
Turns out finding intercepts of a function is done the same way whether you're working with lines or high-power polynomial nightmares. In this chapter, naturally, we'll be working with the easier stuff, though we'll keep revisiting the topic (as will your teacher) for years to come.