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Tonyatodd123 Tonyatodd123
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11 years ago
Find vertical and horizontal asymptotes of (4x)/(x-3)  

How do I find horizontal?
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#1
11 years ago
vertical is x=3 (functional values goes to infinity)
horizontal is the function value when x goes to infinity, in this case y = 4
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#2
11 years ago
vertical asymptotes is when denominator equals to zero

x -3 = 0

x = 3 so asymptotes is at x = 3

Horizontal asymptotes is coefficient of higher term of numerator divided by denominator

as we have horizontal asymptotes is at 4/1

at y = 4
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mhartenburgmhartenburg
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11 years ago
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#4
11 years ago
You divide the coefficients of the highest exponents.  So in this case, the horizontal asymptote is 4x/1x = 4.  Here's the rule:

If the greatest exponent on top is less than that of the one on the bottom, the horizontal asymptote is 0.  Example: (4) / (x+1)

If the greatest exponent on top is equal to that of the one on the bottom, the horizontal asymptote is the division of their coefficients.  Example: (2x -2) / (6x +7) = 1/3

If the greatest exponent on top is greater than that of the one on the bottom, you have no horizontal asymptote; instead you have a slant asymptote and you just do normal polynomial division, usually getting an equation of a line.  Example: (x^2 - 2x +3) / (x+1)
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