How do you identify the horizontal asymptote of $f (x) = \frac{3}{5 x}$ $f(x) = (3)/(5x)$ ?

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How do you identify the horizontal asymptote of $f (x) = \frac{3}{5 x}$ $f(x) = (3)/(5x)$ ?

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Answer 1 · 2015-05-26T14:08:09

Try making $x$ $x$ larger and larger and see where that leads you:

As $x$ $x$ gets larger (either positive or negative) $f (x)$ $f(x)$ gets smaller. You can get as close to $0$ $0$ as you want, but never get there.
So $f (x) = 0$ $f(x)=0$ is the horizontal asymptote .
Or in "the language"
$lim_(x->oo) 3/(5x)=0$ and $lim_(x->-oo) 3/(5x)=0$

Btw: $x=0$ is the vertical asymptote , as $x$ may not be $0$
$lim_(x->0^+) 3/(5x)=oo$ and $lim_(x->0^-) 3/(5x)=-oo$
graph{3/(5x) [-10, 10, -5, 5]}

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How do you identify the horizontal asymptote of $f (x) = \frac{3}{5 x}$ $f(x) = (3)/(5x)$ ?

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