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Sketch a graph of the following function: y= x^2-5x-14/x^2-49 Also include how to...

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danielb77 | Valedictorian

Posted October 21, 2013 at 11:09 PM via web

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Sketch a graph of the following function: y= x^2-5x-14/x^2-49

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 11:26 PM (Answer #1)

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Sketch `y = (x^2-5x-14)/(x^2 - 49)`

x intercept, let y = 0, `(2, 0)`

y-intercept, let x = 0 `(0, 2/7)`

Vertical Asymptotes: x = -7

Horizontal Asymptotes at y = 1.

Long Range Behavior:  `y-> 1 as x->-oo`

`y->1` as `x->oo` , `y->oo as x->-7`

`y->-oo` as `x->-7`

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