Question

Give an example of a rational function that has a horizontal asymptote at y = 1 and a vertical asymptote at
x = 4.

Answer 1

In order for the horizontal asymptote to be the line y = 1, then the coefficients of the numerator and denominator have to be the same as do the powers on the x's. Here's the rule for that:\[f(x)=\frac{ ax ^{n}+... }{ bx ^{m} +...}\]n has to equal m, and the line for the asymptote is y = a/b. So if y = 1, then the a and the b have to be the same number because a number divided by itself is equal to 1.

Answer 2

So what I came up with, really really simple, was this:\[f(x)=\frac{ x+1 }{ x-4 }\]Of course you know that for there to be a vertical asymptote at 4, the denominator would not be allowed to be whatever x value makes the denominator equal 0, which is 4. 4-4=0.

Answer 3

Is this the answer?