00:01
All right, so for problem 747, we're given this function, and we need to find a slant asymptote.
00:07
So before we do that, we need to first check if it actually has a slant asymptote.
00:13
So a function will have a slant asymptote if the degree or the highest exponent of the numerator is larger than the degree of the denominator.
00:23
So the highest exponent of the numerator is 2, and the highest exponent of the denominator of the denominator, is 1.
00:32
So the degree of the numerator is larger than the degree of the denominator, which means there is going to be a slant asymptote.
00:41
And now to find that slant asymptote, there are two ways.
00:44
You basically just divide the numerator by the denominator.
00:50
And like i said, there are two ways to do the long division or synthetic division.
00:54
So first we'll use the long division.
00:59
So you take the divisor x minus 1 you make a division bracket that's what it's called and then you put the dividend inside the bracket so x squared plus 3x minus 3 and now you do the dividing so what do you have to multiply x minus 1 with so that the leading term will be x squared well it's just x since x x times x is x squared so x times x is x squared that's we've just mentioned and and then x times negative 1 is minus x.
01:34
So now we subtract the x squared cancel out.
01:39
And then there's the 3x minus negative x, which is basically plus x.
01:44
So it's going to be 4x.
01:46
And then we bring down the next term, which is negative 3.
01:50
And then we continue.
01:51
So what do you have to multiply x minus 1 so that the leading term is 4x? well, it's just 4.
01:58
So we add plus 4 to the quotions.
02:01
So 4 times x is 4x.
02:05
4 times negative 1 is negative 4, so minus 4.
02:09
And then we subtract.
02:11
So the 4x is cancel out, and negative 3 minus negative 4, or plus 4 is just going to be 1.
02:19
And just like that, we found our slant asymptote, which is y is equal to x plus 4.
02:27
And the remainder that we got, this one here really doesn't matter, so we can just completely ignore it...