00:01
Okay, we need to find the intercepts and the vertical asymptote of this function here.
00:09
Let's start with the vertical asymptote.
00:13
So that's going to occur when the denominator is zero.
00:33
Oops.
00:34
So we can solve that equation and get a value for x.
00:41
I'd add four to both sides, get x equals four.
00:48
So that is the equation actually for the vertical line.
00:54
That is the asymptote.
00:57
Okay, so now let's find the y -intercept.
01:02
So the y -intercept is going to occur when x is 0.
01:14
So to find the y -intercept, we just need to calculate f of 0.
01:26
So we're going to replace all of our x's with 0.
01:36
Okay, so for the numerator, we get 0 squared, which is 0, minus 7 times 0, which is 0, and then we subtract 8 to get negative 8.
01:49
Then in the denominator, we got 0 minus 4, which is negative 4, so f of 0 is 2.
01:57
So the y -intercept is 2...