00:01
Okay, so we have the graph of a rational function, and we want to talk about where that function is greater than zero and where that function is less than or equal to zero.
00:12
Rational functions can change from above the axis to below the axis at two places.
00:19
They can change at vertical asymptopes, and they can change at x intercepts.
00:27
So even if you don't have a graph, if you just have the function, those are the points that you want to.
00:33
Pull out, plot on a number line, and make test intervals around.
00:37
But we have a graph, so it's a little bit easier.
00:40
So where is my function greater than zero? that's another way of saying above the x -axis.
00:49
But remember, we don't want to touch the x -axis because this is greater than, not greater than, or equal to.
00:55
So my graph is above the x -axis here and here.
01:05
Okay.
01:05
So let's say that from next negative infinity until i get to that first vertical asymptote, which is at negative 1, my graph stays above the axis.
01:18
And then you can see at that vertical asymptope, it hops over, right? and then i have a piece below the axis.
01:25
Then at the x intercept, which is at zero, i can see that it starts to go up as well.
01:31
So from zero until the next vertical asymptope, which is at positive 3, it's above the axis.
01:42
Now let's talk about less than or equal to...