SOLUTION: Understanding this graph: http://i.imgur.com/nlOsmHN.png What I don't understand is why does the graph approach from those sides? why not the opposite? why not approach from

Question 916249: Understanding this graph:
http://i.imgur.com/nlOsmHN.png
What I don't understand is why does the graph approach from those sides? why not the opposite? why not approach from the more-negative side of -2 and the positive side of 8? I just I don't remember the rules for this.
Please help
Thank you
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we are given h(x) = 8 - (3 / (2x+4)) which can be rewritten as
h(x) = (16x-29) / (2x+4)
1)The vertical asymptotes come from the zeroes of the denominator, so I'll set the denominator equal to zero and solve.
2x+4 = 0
x = -2
vertical asymptote is -2
note that the range of the function is (-infinity, -2) and (-2, +infinity) which
implies x = -2 is not allowed
2) Since the degrees of the numerator and the denominator are the same (each being 1), then this rational has a non-zero (non-x-axis) horizontal asymptote; the horizontal asymptote is found by dividing the leading terms:
16x / 2x = 8
horizontal asymptote is 8

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