# Asymptotes and functions

## Homework Statement

Make an example of a possible equation whose graph got the asymptotes:
a)
x=3 and y=5
b)
x=-2 and y=3

## The Attempt at a Solution

I have no idea but I'm ready to hear those kind of solutions you might suggest me

## Answers and Replies

you know the asymptote of y = 1/x ? Try moving that graph around

you know the asymptote of y = 1/x ? Try moving that graph around

I've found out a possible solution if we state that x=3 and y=5, then we can say that
x-a=0
x-3=0
x=3
then we can put our value in and put it under our fraction so we now got:

( )/3-x

Nothing in the parantese:
Now we need the y asymptote:

y=5
f(0)=5 to make this statement true:
We need to say that:
(5x/x)/(3/x - x/x)
x-> eternity
so 3/x will be close to zero and in math = 0
so we got 5/1 = 5 this equals true. So our possible equation for our asymptotes:

5x/(3-x).

Is there some errors in my solving this equation or is this a possible answer?

Edit: Had a wrong function with the wrong sign; mrkuo is correct.

Another one which came to mind first was 1/(x-3) + 5. This is just a shifting of the graph of 1/x.

Last edited:
Unfortunately,

y=5x/(3-x)

will not produce the asymptotes x=3 and y=5, rather, x=3 and y= negative 5.

Use y = 5x/(x-3) instead. Previous poster's answer works just as well.