Question 1151184
Given a function and the corresponding reciprocal function, the graph of the reciprocal function will have vertical asymptotes where the function has zeros (the x-intercept(s) of the graph of the function).


so, {{{x=-1}}} and {{{ x=2}}} are x-intercept: ({{{-1}}},{{{0}}}), ({{{2}}},{{{0}}}) 

so, use root product theorem to find equation first

{{{y=(x-(-1))(x-2)}}}

{{{y=(x+1)(x-2)}}}



so,  when it is reciprocated we have

f(x)=1/y

f(x)=1/((x+1)(x-2)) for {{{x<>-1}}} and {{{x<>2}}}

note: the vertical asymptotes  are the values that are not allowed in the domain, they are in denominator

so, {{{x=-1}}} and {{{ x=2}}} are asymptotes


 {{{drawing( 600, 600, -10, 10, -10, 10,
line(-1,10,-1,-10),line(2,10,2,-10),locate(3,3,red(y=(x+1)(x-2))),locate(2,-3,green(y=1/((x+1)(x-2)))),
 graph( 600, 600, -10, 10, -10, 10, (x+1)(x-2),1/(x+1)(x-2))) }}}