Sketch a graph of the following function: y= x^3-3x^2/x^2+x-20
Also include how to determine the a)x- and y- intercepts (if any)
b) Vertical Asymptotes and/ or Holes (if any)
c) Long Range Behaviour
d) Points at which the graph crosses its Horizontal or Slant Asymptote (if any)
Sketch a graph of `y = x^3 - (3x^2)/(x^2 + x -20)`
`y = x^3 - (3x^2)/((x+5)(x-4))`
x-intercepts, let y = 0 (0,0)
y-intercepts, let x = 0 (0,0)
Vertical asymptotes at x = -5 and x = 4
Long term behavior: `y->-oo` as `x->-5,`
`y->oo, as x->4` .
See image for graph.