SOLUTION: find the specified asymptotes of the following functions, recall the asymptotes are lines therefor the answer must be given as an equation of a line. a.Find the equation o

Question 452409: find the specified asymptotes of the following functions, recall the asymptotes are lines therefor the answer must be given as an equation of a line.

a.Find the equation of the vertical a asymptotes of the function f (x) = 4/x+5
b. Find the equation of the horizontial asymptote of the function g (x) = 5x^2 -4/x+1
c. Find the equation of both the vertical and horizontal asymptotes of the function f (x) = 3x-1/x+4

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Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
a.Find the equation of the vertical a asymptotes of the function f (x) = 4/x+5
b. Find the equation of the horizontial asymptote of the function g (x) = 5x^2 -4/x+1
c. Find the equation of both the vertical and horizontal asymptotes of the function f (x) = 3x-1/x+4
..
a. f (x) = 4/x+5
To find the vertical asymptote, set the denominator=0, then solve for x.
For given equation:
x+5=0
x=-5
Equation of vertical asymptote: x=-5
..
b. g (x) = 5x^2 -4/x+1
If degree of numerator>degree of denominator,as in this case, you get a slant asymptote.
By long division divide numerator by denominator. In this case you will get a quotient=5x-5 plus remainder -1. Equation of the slant asymptote is a line:y= 5x-5
..
c.f (x) = 3x-1/x+4
If degree of numerator and denominator are the same, the horizontal asymptote is equal to lead coefficient of numerator divided by the lead coefficient of denominator.
Equation of horizontal asymptote: y=3/1=3
Note: If degree of numerator< denominator, the horizontal asymptote is the x-axis or y=0
x+4=0
x=-4
Equation of vertical asymptote: x=-4
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