SOLUTION: 5) Find the equations for the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote. a)f(x)=2x+1/x-4 Answer: Horizont

Question 136860: 5) Find the equations for the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.
a)f(x)=2x+1/x-4
Answer:
Horizontal:
Vertical:
b) g(x)=3X/X^2+4
Answer:
Horizontal:
Vertical:

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Vertical asymptotes are defined by the equation where a is a value that would make the function undefined. In these two cases, values that would make the denominator go to zero.

Horizontal asymptote. There is either one or none for any given rational function.

If the degree of the denominator polynomial is greater than the degree of the numerator polynomial, then the horiziontal asymptote is

If the degree of the denominator polynomial is equal to the degree of the numerator polynomial, then the horizontal asymptote is where p is the lead coefficient of the numerator and q is the lead coefficient of the denominator.

If the degree of the denominator is less than the degree of the numerator, then there is no horizontal asymptote. If the degrees differ by 1, there is a straight line oblique asymptote whose equation is equal to the quotient excluding the remainder when the numerator is divided by the denominator using polynomial long division.
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