00:01
So in this problem, we're given the rational function f of x, and the first thing we want to do is find the vertical asymptopes.
00:06
Well, remember, before you find your vertical asymptopes, what you should do is simplify your original expression.
00:12
I notice in this case that we can factor our denominator, because that's an example of the difference of two squares.
00:18
So our numerator will stay the same, x plus 10, and then we'll factor our denominator.
00:23
Well, the square root of x squared is x, so they both start with x.
00:26
The square root of 100 is 10, so they both have with 10.
00:28
And then remember one signs positive and the other is negative.
00:32
Notice we now have the common factor in the numerator denominator, so these terms will cancel each other out, which leaves us with 1 over x minus 10.
00:40
Now that we have our simplified expression, we can go ahead and find our vertical asymptotes.
00:45
Our vertical asymptotes will occur when our denominator is equal to 0.
00:48
So we'll set x minus 10 equal to 0, so to solve for x, we just add 10 to both sides.
00:54
So now we know that we have a vertical asymptote when x is equal to 10.
00:58
Next, what we want to do is find any slope or horizontal or oblique asymptotes...
