How do you identify the horizontal asymptote of #f(x) = (3)/(5x)#?

1 Answer
MeneerNask
May 26, 2015

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

As #x# gets larger (either positive or negative) #f(x)# gets smaller. You can get as close to #0# as you want, but never get there.
So #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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