Question 1137488


make a graph of 

{{{f(x)= (x+3)/(x^2+x-12)}}}

{{{f(x)= (x+3)/(x^2-3x+4x-12)}}}

{{{f(x)= (x+3)/((x^2-3x)+(4x-12))}}}

{{{f(x)= (x+3)/(x(x-3)+4(x-3))}}}

{{{f(x)= (x+3)/((x + 4) (x - 3))}}}



asymptotes:

Horizontal asymptote: {{{y=0}}}

{{{(x + 3)/(x^2 + x - 12)->0}}} as {{{x}}}-> ± {{{infinity}}}

Vertical asymptotes: {{{x=-4}}} and {{{x=3}}}

{{{(x + 3)/(x^2 + x - 12)}}}-> ± {{{infinity}}} as {{{x->-4}}}
{{{(x + 3)/(x^2 + x - 12)}}}-> ± {{{infinity}}} as {{{x->3}}}

domain: 
{ {{{x}}} element {{{R}}} : {{{x<>-4}}} and {{{x<>3}}} }

the {{{x}}} intercepts:

{{{x+3=0}}} =>{{{x=-3}}}

the {{{x}}} intercepts:( {{{-3}}},{{{0}}}) 

the {{{y}}} intercept: 

{{{f(0)= (0+3)/(0^2+0-12)=3/-12=-1/4}}}

 ({{{0}}}, {{{-1/4}}})



{{{drawing ( 600, 600, -10,10, -10, 10,
blue(line(-4,10,-4,-10)),blue(line(3,10,3,-10)),
circle(0,-1/4,.12),circle(-4,0,.12),circle(3,0,.12),
graph( 600, 600, -10,10, -10, 10, (x+3)/(x^2+x-12),0)) }}}