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

Only two requirements? Write as quickly as you can read the problem statement!

\(y = \dfrac{x+2}{x-4}\)

There are many, MANY other options.

The important parts are these.
1) Get x-4 in the denominator.
2) Make sure the numerator has the same degree as the denominator.
3) Make sure the leading coefficients are the same.

Another example:

\(y = \dfrac{(3x+2)^{2}}{9(x-4)(x+6)}\)

Like I said, LOTS of possibilities - infinitely many, in fact.

Answer 2

The only thing I don't understand is what to do with y=1

Answer 3

That's what my notes 2 and 3 are all about.

2) Make sure the numerator has the same degree as the denominator.
3) Make sure the leading coefficients are the same.

Answer 4

#2 makes sure the asymptote is Horizontal.
#3 makes sure it is at y = 1.