Graphing Absolute Values Part 1 y = |x|

Uploaded by MATHRoberg on 09.09.2010

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.