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

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Answer 1 · 2017-01-08T15:53:03

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

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]}

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