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Home Q & A Board Science-Related Homework Help Mathematics
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budababie budababie
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10 years ago
in the problem x+1/x(x+4) what is the horizontal asymptote?

The back of the book says there is none, but I'm confused by that.
how is y=0 the same thing as having no y intercept though? or no horizontal asymptote.
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#1
10 years ago
The book is correct...If you had been given the function (x+1)/(x+4), that is, without the extra factor 'x', then the horizontal asymptote would be y=1...But in order to have a horizontal asymptote you need the largest powers of both numerator and denominator to have the same exponent...
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#2
10 years ago
If you distribute the x on the bottom of the expression to the x+4, you will have (x+1)/(x^2+4x). Since the degree (highest exponent) of the bottom is higher than that of the top, the function has no horizontal asymptote. If the degree of the top were higher, then the function would have a horizontal asymptote at y=0. If the degrees of the top and bottom were the same, then the horizontal asymptote would be at the ratio of the coefficients of the highest degree term in each part. For example, if you had (2x+1)/(3x+4), the horizontal asymptote would be at y=2/3
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mhite7mhite7
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10 years ago
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