Absolute Value Functions

So we have worked on absolute values and we've talked about functions.
WHICH WAS A HOOT!

But now we should talk about another thing. The "Chapter" is called Absolute Value Functions but it would be more accurate to call it graphing absolute values.

Let's look at a build of a Absolute Value equations

4|x+3|-5 = y

Now let's replace that with variables.

a|x-h|+k = y

a = 4

-h = 3

k = -5

This is the basic build of an Absolute Value Function. This is also very important in graphing. HEre is the graphing of the equation.

If you look at the vertex you will see that it's coordinates are (-3,-5). In Absolute Value Equations, The vertex is always (-h,k) and the slope is a.

Functions and their Graphs

A relations is a mapping of input and output values. The set of input values is the domain and the set of output values is the range.

So what is a function? Well a function is a relation that has an outcome that is predictable. What does that mean?

Well look at these three situations

Every time you give 75 cents, you get 1 coke. 

If you give 75 cents you will get either no cokes, 1 coke or 2 cokes.

No mater how much you give, you get a coke.

Which ones are actually predictable? 

That's right, the 1st and 3rd one! Why?

Because no matter what, you know what your out put will be. For the first one you know the outcome will always come the one input. As for the third one, you always know what is going to come out.

So what is a good way to test this? Well there are two ways.

One way is to graph the points and put lines through each point. If a line passes two points, it is not a function.

Another is to separate the input and outputs and match them, to see if one input has two outcomes.