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

@dude

Answer 2

So the same concept the denominator cannot equal 0 to get a vertical asymptote
If \(\frac{1}{(x-1)}\) creates an asymptote at x=1, how would you get an asymptote at x=4?

Answer 3

1 over (x-4)?

Answer 4

Vertical asymptote^

Answer 5

Right

Answer 6

so would the answer be f(x)=1 over (x-4)?

Answer 7

Not quite, we are still looking for a horizontal asymptote at y=1

Answer 8

so how do i get that?

Answer 9

Right now \(\frac{1}{x-4}\) Gives a horizontal asymptote at 0, do you have an idea on how to increase it by 1?

Answer 10

ad one to the top?

Answer 11

Right now \(\frac{1}{x-4}\) Gives a horizontal asymptote at 0, do you have an idea on how to increase it by 1?

The function is written as \(f(x)=\frac{a}{x-h}+k\) (Hint k translates up)
Which is now \(f(x)=\frac{1}{x-4}+0\)
Do you know how to translate it?

Answer 12

No i dont

Answer 13

Add 1 to k x'D
\(f(x)=\frac{1}{x-4}\color{green}{+1}\)

Answer 14

ok awesome thanks lol

Answer 15

i got one more can you help

Answer 16

Sure make a new post