00:01
Okay, for problem 34, they give us a rational function, so a polynomial divided by a polynomial, and in this case it's a linear function divided by a quadratic.
00:11
They want us to find the vertical asymptotes.
00:13
Now, vertical asymptotes occur when we have division by zero.
00:19
And there's one extra stipulation where this does not occur.
00:25
So where you cannot cancel any terms.
00:32
Or i'm going to say remove any variable factors.
00:38
So what that essentially means is if i can factor the top and bottom and cancel a factor, so something like x plus or minus a number divided by x plus or minus that same number, if i have the same factor divided by itself, i can cancel that out, right? the division by itself always equals one, which would make whatever this number is, the plus or minus, that would be a removable discontinuity, otherwise known as a missing point or a hole discontinuity.
01:07
So whole and or missing point depending on what terminology you were taught.
01:13
So i always referred to it as a whole.
01:17
So what we need to do for this particular example, i'm going to factor the top is already as factored as it can get, but the bottom i'm going to factor 2x squared and see if there's any terms that will cancel.
01:30
So 2x squared minus 6x minus 8.
01:33
Well, first of all, i see that there's 2, 6, and 8.
01:36
So i can factor a 2 out right away.
01:39
That's my greatest common factor.
01:42
So i have 2 times x squared minus 3x minus 4.
01:46
And then i can see right away, i like to think about factoring as unfoiling.
01:51
So this is the product of foiling, the result, right? so this is first times first, this is last times last.
01:56
This is outer plus inner.
01:58
So i need to figure out what numbers when they're multiplied together, they give me the last term, and when they're added together, they give me that middle term of negative 3.
02:07
So that's going to be negative 4 and 1...