00:01
This problem wants us to find all vertical and horizontal asymptotes of the graph of the function, and our function is f of x equals 5 plus x divided by 5 minus x, and we also want to look at how we find the horizontal asymptotes.
00:13
So first for the vertical asymptotes, vertical asymptotes are occurring when you have an x value that turns your denominator to zero, because when you divide by zero, you get undefined values.
00:24
So to find those x values that create vertical asymptotes, you can set your denominator expression equal to zero, and solve for x, and this will solve pretty quickly once we add x over to the right side, that will tell us that 5 equals x or x equals 5.
00:38
So a vertical asymptote we have is x equals 5.
00:41
For our horizontal asymptote, there's several rules you need to focus on for horizontal asymptotes because it all depends on what the degree of the numerator and the degree of the denominator is.
00:52
And to make this a little easier, what we're going to do is rewrite our function to be in standard form for our expression on the numerator and denominator.
01:02
So for f of x, we're going to write this instead of 5 plus x, we're going to write it as plus x plus the positive 5, divided by instead of 5 minus x, negative x plus the positive 5...