3.4 Definition of a Function

Before you go on to read this chapter, you should understand the most

PROFOUNDLY IMPORTANT thing that Mr. Wilhelm will tell us. Here it is: f(x)=y

The textbook almost always uses f(x), but have no fear.

These ideas of fear you may have rest in the fiery pits of hell for they will do you no good.

They will confuse you and tell you that math isn't your friend. And that is the biggest lie ever told.

Math is your friend.

Now that we have gotten past that obstacle, we can talk about the subject of the chapter. Functions.

The book definition of a function is pretty complicated and mean. So here's a simplified one.

Function- every x corresponds to exactly one y.

Simple. But we have to not be fooled by the evildoings of correspondences that aren't functions.

For instance, f(x) = x² is a function because every x has one y.

ex. 4=2², 4=-2²

But y²=x is not a function. it can be simplified to y=. It has 2 y's for every x.

ex. 2=√4 and -2=√4. Unacceptable.

2 cannot equal bicycle and motorcycle.

In a function, the possible values of x is called the domain.

The possible values of y is the range. Fun.

In the mysterious land of math, there is a magical game called the vertical line test.

Here's how it goes. If no two points are on any vertical line on the graph, it's a function.

If two or more points are on a vertical line........ NOT A FUNCTION

This is a function with domain [-2π, 2π] and range [-1, 1].

So I think we all learned a little something today. Yep.