How do you find the vertical, horizontal or slant asymptotes for # y = 4/(x - 3)#?

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Answer 1 · 2017-02-12T07:06:41

The vertical asymptote is #x=3#
The horizontal asymptote is #y=0#
No slant asymptote

As you cannot divide by #0#, #x!=3#

The vertical asymptote is #x=3#

The degree of the numerator is #<# than the degree of the denominator, there is no slant asymptote.

#lim_(x->-oo)y=lim_(x->-oo)4/x=0^-#

#lim_(x->+oo)y=lim_(x->+oo)4/x=0^+#

The horizontal asymptote is #y=0#

graph{(y-(4/(x-3)))(y)(y-300x+800)=0 [-11.25, 11.245, -5.63, 5.62]}