vertical asymptotes at ±5 horizontal aymptote at y = 0.2 (toughie: if degree numerator = degree denominator then horizontal asymptote is lead coefficient ratio) y-intercept = 36/125 x-intercepts (Maxima) (%i3) solve([(x^2-36)/(5*x^2-125)=0], [x]); (%o3) [x=-6,x=6]
vertical asymptotes at ±6 horizontal aymptote at y = 0 (x-axis) y-intercept = 1/6 x-intercepts at x = -1
vertical asymptotes at x = −3, x = 5 horizontal aymptote at y = 0 (x-axis) y-intercept = -2/15 x-intercept = -2
reset set border set xtics 1 set ytics 1 set xzeroaxis lt 9 lw 5 set yzeroaxis lt 9 lw 5 set style line 1 lt 1 lw 2 set style line 2 lt 3 lw 3 set style line 3 lt 10 lw 4 set style line 4 lt 12 lw 3 set style line 5 lt 9 lw 1 set grid ls 5 show grid set xrange [-8:8] set yrange [-4:4] set samples 1000 set key on f(x)=(x**2)/(5*x**2-125) g(x)=(x+1)/(sqrt(36-x**2)) h(x)=(x+2)/(x**2-2*x-15) plot f(x) ls 1,g(x) ls 2, h(x) ls 3