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)
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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) (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 , the leading coefficient is
Looking at the denominator , the leading coefficient is
So the horizontal aysmptote is the ratio of the leading coefficients. In other words, simply divide by to get
So the horizontal asymptote is
Vertical Asymptote:
To find the vertical aysmptote, just set the denominator equal to zero and solve for x
Add 1 to both sides
Combine like terms on the right side
So the vertical asymptote is
Notice if we graph , we can visually verify our answers:
Graph of with the horizontal asymptote (blue) vertical asymptote (green)
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