Question 1187377
Give the domain, intercepts, asymptotes, and range of 

{{{f(x)=(2x-1)/(x^2-4)}}}

the domain will be all {{{x}}} except the values that makes denominator equal to zero and these values are

{{{x^2-4=0}}}
{{{x^2=4}}}
{{{x=sqrt(4)}}}

solutions: {{{x=2}}} or {{{x=-2}}}

domain:{ {{{x}}} element {{{R}}} :{{{ x<>-2}}} and {{{x<>2}}} }
 
range: {{{R}}} (all real numbers)

Horizontal asymptote:

{{{(2x - 1)/(x^2 - 4)->0}}} as {{{x}}}-> ± {{{infinity}}}

Vertical asymptote: {{{ x=-2}}} and {{{x=2}}} }


{{{ drawing( 600, 600, -10, 10, -10, 10,
green(line(-2,10,-2,-10)),green(line(2,10,2,-10)), 
graph( 600, 600, -10, 10, -10, 10, (2x-1)/(x^2-4),0 )) }}}