00:02
This question asks us to write a function that satisfies all of these different criteria.
00:09
So we have a vertical asymptote at x equals negative 1 and at x equals positive 3.
00:15
So i'm going to start by creating my rational function.
00:20
And vertical asymptotes come from setting the denominator equal to 0.
00:25
So i have to think backwards here and think what factor if i set it equal to 0? would have an answer of negative 1.
00:37
That will be x plus 1.
00:40
Same thing for the x is equal to 3.
00:43
What factor if said equal to 0 would have an answer of x equals 3? x minus 3, set equal to 0.
00:53
Okay, my horizontal asymptote is at 2.
00:56
So that means that the ratio of my leading coefficients is going to be 2.
01:02
So i technically already have a coefficient of a 1 in my denominator.
01:06
So i'm going to put a two in my numerator.
01:11
2 divided by the one that's down in my denominator is 2.
01:15
I want x intercept at negative 2 and at positive 1.
01:20
So x intercepts come from setting the numerator equal to 0, the same way we were doing the denominator for the vertical asymptotes...