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Sketch a graph of the following function: y= x^3-3x^2/x^2+x-20 Also include how to...

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danielb77 | Valedictorian

Posted October 21, 2013 at 11:01 PM via web

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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) 

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted October 21, 2013 at 11:14 PM (Answer #1)

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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.

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