Question

What is the domain and range of `y = (x + 3) / (x -5)`?

Answer 1

Domain: `(-oo,5)uu(5,oo)`
Range: `(-oo,1)uu(1,oo)`

Explanation:

Ok, lets start with the Domain
The domain of this equation is all numbers except when you divide by `0`. So we need to find out at what `x` values does the denominator is equal to `0`. To do this we simply we the denominator equal to `0`. Which is

`x-5=0`

Now we get `x` alone by adding `5` is both sides, giving us
`x=5`

So at `x=5` this function is undefined.
That means that every other number you can think of will be valid for this function. Which gives us `(-oo,5)uu(5,oo)`

Now to find the Range
The range can be found by dividing the leading coefficients from the numerator and the denominator. In the numerator we have `x+3` and in the denominator we have `x-5`

Since there is no number in front of the `x` values we just treat it as `1`

So it would `1/1` which is `1`.
So the range is `(-oo,1)uu(1,oo)`