Uploaded by MATHRoberg on 09.09.2010

Transcript:

Let's talk about the graph of the absolute value parent function, but first, let's just talk about the graph of y = x.

Now, the easiest way to graph this for me is just to notice that whatever x is, y is going to be also.

So, for example, when x is 2, y will also be 2.

...and when x is 0, y will be 0.

How about when x is 5?

y will also be 5.

And what about when x is -2?

Well, y will be -2.

When we graph this...we can see that it creates a line, and the line has a slope of 1.

That's consistent if we think of this as slope-intercept form.

y = mx + b.

Up here, the slope is 1, and the y-intercept, b, is 0.

So, that's why we have this line.

Now, let's think of the parent function for absolute value.

What if we were to graph y = the absolute value of x?

Now, this looks very similar to y = x, except for this absolute value sign.

Let's see how that changes things.

Over here, in Quadrant 1, when x is positive, y is still going to positive and the same thing as x.

For example, when x is positive 2, y is positive 2.

...and when x is 6, y is 6.

Well, what about when we talk about negative x's?

When x is -1, the absolute value of -1 is positive 1.

So we have the coordinate (-1,1).

What about when x is -3?

When x is -3, y is going to equal 3.

Graphing this will end up looking like this.

So, over here matches the graph of y = x, but the graph of y = x went down into quadrant 3 here.

It's being reflected up here because now every negative y is going to be a positive y instead.

Now, the easiest way to graph this for me is just to notice that whatever x is, y is going to be also.

So, for example, when x is 2, y will also be 2.

...and when x is 0, y will be 0.

How about when x is 5?

y will also be 5.

And what about when x is -2?

Well, y will be -2.

When we graph this...we can see that it creates a line, and the line has a slope of 1.

That's consistent if we think of this as slope-intercept form.

y = mx + b.

Up here, the slope is 1, and the y-intercept, b, is 0.

So, that's why we have this line.

Now, let's think of the parent function for absolute value.

What if we were to graph y = the absolute value of x?

Now, this looks very similar to y = x, except for this absolute value sign.

Let's see how that changes things.

Over here, in Quadrant 1, when x is positive, y is still going to positive and the same thing as x.

For example, when x is positive 2, y is positive 2.

...and when x is 6, y is 6.

Well, what about when we talk about negative x's?

When x is -1, the absolute value of -1 is positive 1.

So we have the coordinate (-1,1).

What about when x is -3?

When x is -3, y is going to equal 3.

Graphing this will end up looking like this.

So, over here matches the graph of y = x, but the graph of y = x went down into quadrant 3 here.

It's being reflected up here because now every negative y is going to be a positive y instead.