00:01
So in this problem, we're being asked to determine which of the following equations could possibly represent this graph.
00:06
All right.
00:06
Well, first off, let's think about what our typical log -based 2 of x graph looks like.
00:10
Remember, it would have a vertical asymptote at y -equal 0, and it would cross our y -axis here at 1, or our x -axis at 1.
00:18
So our typical log function looks like this.
00:21
And i know my graph isn't going to be the greatest, but essentially it's increasing until it gets here.
00:25
We have a vertical asymptote.
00:27
Okay.
00:28
Well, notice that this graph got reflected over.
00:30
Over the, and almost kind of forget that this part here exist.
00:34
So this graph definitely got reflected over the x -axis, which is why for each of these functions there's a negative at the beginning.
00:41
So that part's true.
00:42
Well, notice that compared to here, it got shifted over our vertical asymptote, two units to the left.
00:51
So again, to show that this got shifted over two units to the left, that means inside our preemphasies, we would have to have x plus two.
00:56
So these two graphs with x minus two would have to cancel out.
00:59
Okay, so now we just have to see which of these would work.
01:03
So what we can do is we can substitute these points in.
01:06
So i'm going to substitute in this point, negative 1, 5, and see which one makes it true.
01:12
So if i go for the first one, that would mean that we have 5 equal to negative 1 1⁄2 of negative 1 plus 2 plus 5.
01:24
All right, so first we have negative 1 plus 2, which is equal to 1...