00:01
So i have a rational function, and in order to identify the domain and some of the features of the graph, i'm going to want to factor this.
00:10
So let's factor the numerator.
00:12
I get 2x and x, and that's 2 and 2.
00:19
To get my 4x on the outside, 2x on the inside, that'll give me a 6x middle term.
00:26
Okay, on the bottom i'm going to factor that.
00:30
That is x minus 3 x plus 1 okay i can keep going in my numerator pull that 2 out now i have 2 times x plus 1 times x plus 2 over my denominator okay now my function is fully um factored so i can state my domain and in set notation, i'm going to have to take out any values that make my denominator zero.
01:03
That's going to be negative one and three.
01:06
If i want to write that as an interval, right, or as an interval, that would be negative infinity to negative one, negative one to three, three to infinity, and connect them with a union symbol.
01:24
Okay.
01:25
Now before i identify vertical asymptopes or holes, i want to look at my function and i want to cancel any common factors.
01:34
So i have x plus one to cancel on top and on the bottom.
01:39
That leaves me with this as a simplified function.
01:44
Now it's in what we call lowest terms...