Waching daily Jul 3 2018

This video is about the absolute value function.

This function is written, "f of x equals absolute value of x," or "y equals absolute value of x."

So let's just briefly review what we mean by absolute value.

Absolute value is your distance from zero. If you think of the number line - I'll put some numbers on it -

and we say something like, "the absolute value of 2," 2 is 2

units away from zero, so the absolute value of 2 equals 2.

Now if we look at negative 2,

we can also say that

negative 2 is 2 units away from 0, so we say the absolute value of negative 2 is also positive 2. So

the absolute value is always going to be positive unless, of course, you have 0. 0 is 0 units away from

0, so when we fill in the table here the absolute value of 0 is going to be 0,

the absolute value of 1 will be 1. 2 will be 2,

etc. When you get to a negative number the absolute value of the negative 1 will be positive 1,

absolute value of negative 2 is positive 2,

positive 3, point 5, and positive point 5.

Now, if we go ahead and graph these,

well, first, before we graph let's think of something for a minute. Here,

if we look at this table:

(0, 0), (1,1), ( 2, 2), (3,3), it looks very similar to our identity table when we had positive values of x.

So when our X-values are positive, if you can remember what that identity graph looked like, it should look pretty much the same

with our absolute value. Now when we get into the negative values of X down here,

now we're going to have positive values of Y, so this is going to be a little bit different than what we had before.

So let's go. Let's see what we get. We get (0, 0),

(1, 1), (2, 2), (3, 3) and

four positive values of X. This does look like a straight line that cuts

Quadrant 1 in half, just like the identity function did. And for the negative values of X we get (negative 1, positive 1), (negative 2, positive 2),

(negative 3, positive 3), and

if we graph that,

It also looks like it's cutting the quadrant in half.

But instead of cutting Quadrant 3 in half, like we did with our identity function, because our Y values are now positive,

we're cutting Quadrant 2 in half. We have to move that

line up until the second quadrant, and so we get this typical v-shape that we get whenever we make an

absolute value graph.

So, let's write this in here:

absolute value.