How do you graph $y=(8x+3)/(2x-6)$ using asymptotes, intercepts, end behavior?

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Answer 1 · 2016-11-20T09:50:08

See the graph below

The domain of $y,$ $D_y=RR-{3}$

As we cannot divide by $0$ , $x!=3$

A vertical asymptote is $x=3$

For the limits, we take the terms of highest coefficients in the numerator and the denominator

$lim_(x->+-oo)y=lim_(x->+-oo)(8x)/(2x)=4$

A horizontal asymptote is $y=4$

For the intercepts,

$x=0$ , $=>$ , $y=3/-6=-1/2$

This is the y-intercept $(0,-1/2)$

When $y=0,$ => $,$ x=-3/8#

This is the x-intercept, $(-3/8,0)$

$lim_(x->3^(-))y=-oo$

$lim_(x->3^(+))y=+oo$

graph{(y-(8x+3)/(2x-6))(y-4)(x-3)=0 [-22.8, 22.85, -11.4, 11.4]}

How do you graph y=(8x+3)/(2x-6)y=(8x+3)/(2x-6) using asymptotes, intercepts, end behavior?