00:01
For this problem, we are going to graph this pair of functions on the same set of coordinate axes.
00:07
And then we're going to find their ranges.
00:10
So let's get started.
00:11
Looking at these two functions, f of x is equal to absolute value of x.
00:16
That's actually going to be apparent function.
00:19
So that's the one that will graph first.
00:22
And then we'll do some sort of transformation to get g of x.
00:26
So absolute value of x, what does that look like? well, no matter what you stick into an absolute value, your output is going to be not negative.
00:36
So it is mostly going to reside in the upper half of our x, y, plane.
00:43
And it's also going to look like a v.
00:46
So it looks something like this.
00:49
Let's see if i can try to draw straight here.
00:52
Straight as can be anyways.
01:00
So this right here is our f of x is equal to the absolute value of x.
01:04
So that is our apparent function.
01:10
Now to get to g, the only difference or the only change is that we have this minus 3 here.
01:16
Minus 3 here on the outside of the opposite values is a vertical shift.
01:22
And since we're subtracting 3, it's a vertical shift downwards by 3.
01:27
So instead of having our pointed part right here at the origin, it's now going to be at 0 negative 3.
01:37
So this point right here, and then all of the points subsequently are going to be three units lower than what they were.
01:45
So again, we're going to have that v shape, but lower down...