SOLUTION: Find the horizontal and vertical asymptotes of the following. Type “none” if the function does not have an asymptote. b)g(x)=5x/(x-1)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the horizontal and vertical asymptotes of the following. Type “none” if the function does not have an asymptote. b)g(x)=5x/(x-1)      Log On


   

Question 115519: Find the horizontal and vertical asymptotes of the following. Type “none” if the function does not have an asymptote.

b)g(x)=5x/(x-1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
b)
Horizontal Asymptote:
To find the horizontal aysmptote, first we need to find the leading coefficients of the numerator and the denominator.

Looking at the numerator 5x, the leading coefficient is 5

Looking at the denominator x-1, the leading coefficient is 1

So the horizontal aysmptote is the ratio of the leading coefficients. In other words, simply divide 5 by 1 to get %285%29%2F%281%29=5


So the horizontal asymptote is y=5




Vertical Asymptote:
To find the vertical aysmptote, just set the denominator equal to zero and solve for x

x-1=0


x=0%2B1Add 1 to both sides


x=1 Combine like terms on the right side


So the vertical asymptote is y=1


Notice if we graph y=%285x%29%2F%28x-1%29, we can visually verify our answers:

Graph of y=%285x%29%2F%28x-1%29 with the horizontal asymptote y=5 (blue) vertical asymptote x=1 (green)