Homework 20080708

$\text{f(x)}=\frac{x^2-36}{5x^2-125}$

 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]
 

$\text{g(x)}=\frac{x+1}{\sqrt{(36-x^2)}}$

 vertical asymptotes at ±6
 horizontal aymptote at y = 0 (x-axis)
 y-intercept = 1/6
 x-intercepts at x = -1
 

$\text{h(x)}=\frac{x+2}{x^2-2x-15}$

 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