Question

What is the range of the function `f(x) = 5/(x-3)`?

Answer 1

The range of `f(x)` is `R_f(x)=RR-{0}`

Explanation:

The domain of `f(x)` is `D_f(x)=RR-{3}`

To determine the range, we calculate the limit of `f(x)` as `x->+-oo`

`lim_(x->-oo)f(x)=lim_(x->-oo)5/x=0^-`

`lim_(x->+oo)f(x)=lim_(x->+oo)5/x=0^+`

Therefore the range of `f(x)` is `R_f(x)=RR-{0}`

graph{5/(x-3) [-18.02, 18.01, -9, 9.02]}