How do you find the domain and range of #g(x)= (3x)/(2x-5)#?

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Answer 1 · 2015-07-19T12:03:29

For the domain there is only the restriction that #x!=2 1/2#
This would make the numerator #=0#

In the "language" we say:

#lim_(x->2 1/2) g(x)= oo# and #x=2 1/2# is the vertical asymptote

As #x# gets larger the function will tend to look more and more like

#(3x)/(2x)=1 1/2# without quite getting there, or:

#lim_(x->oo) g(x)=1 1/2# or #g(x)=1 1/2# is the horizontal asymptote

So the range has as only restriction #g(x)!=1 1/2#

graph{3x/(2x-5) [-10.98, 21.04, -5.92, 10.1]}