# 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...

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)

### 1 Answer | Add Yours

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.