# 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...

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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Expert Answers

baxthum8 | Certified Educator

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`