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]}

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