00:01
This problem wants us to come up with the function for a rational function where we're given some information about it, and we're told that the vertical asymptotes are x equals 1 and 6.
00:09
We have a horizontal asymptote of y equals 0 with no x intercept, but our rational function is supposed to travel through 5 .1.
00:15
So we'll begin to build our function by writing our vertical asymptotes first, and that would come in the form of two binomials in the bottom of our fraction.
00:25
So x minus 1 would give us a vertical asymptote of 1, and x minus 6 would give us a vertical asymptote of positive 6.
00:33
And since we're told there's no x intercept, we know that there can't be an x value on top of our function, so this has to be some constant.
00:40
We'll label it as a.
00:41
And right now we don't have a lot of information to finish, but we are told it's supposed to go through the 0 .51.
00:47
So what we can do is assume that our form now can equal 1 when we evaluate it at 5.
00:53
And if we evaluate at 5, then we will have only one unknown, which is the a, and hopefully we'll be able to solve for a to make it true where it's equal to 1...