<prompt> Grafu ya chaguo za kukokotoa kimantiki fracpxqx imeonyeshwa hapa chini. Ikiwa qx ni quadratic, p33, na q2 2, pata px qx.asyukubwa 8cm;kuagiza grafu;Lebo f;f.pfontsize6;xaxis-5,5,Ticksf, 1.0;yaxis-5,5,Ticksf, 1.0;chora-5,0--5,0;chora0,-5--0,5;int i;kwa i -5; i 5; i ikiwa i! 0 chorai,-0.2--i,0.2; chora-0.2,i--0.2,i; lebo stringi , i,-0.2, S; lebo stringi , -0.2,i, W; f halisi x halisi kurudi xx-1x;choragrafuf,-5,-3.5, iliyopigwa;choragrafuf,-3.5,-0.1;choragrafuf,0.1,0.7;choragrafuf,0.7,0.8, iliyokatika;kuchora grafuf,1.2,1.3, iliyopigwa;choragrafuf,1.3,3.5;kuchora grafuf,3.5,5, iliyopigwa;filldrawmduara0,-1,.15,nyeupe;asy  <response>: Kwa kuwa qx ni quadratic, na tuna asymptote mlalo kwa y0, tunajua kwamba px lazima iwe mstari.Kwa kuwa tuna shimo x0, lazima kuwe na kipengele cha x katika px na qx. Mwisho, kwa kuwa kuna asymptote wima x1 , the denominator qx lazima iwe na kipengele cha x-1. Kisha, px ax na qx bxx-1, kwa baadhi ya vipengele a na b. Kwa kuwa p3 3, tuna 3a 3 na hivyo a1. Tangu q2 2, tuna 2b2-1 2 na hivyo b1.Kwa hivyo px x na qx xx - 1 x2 - x, na px qx x2. 