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Question 787302: sketch the graph of each rational function:
3x - 4 / 10x^2 - 21x - 10
find vert. asymptote
horiz. asymptote
y-intercept
x-intercepts
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Vertical asymptotes occur where the denominator function has a real zero. Set the denominator equal to zero and find all real number zeros. Let's say the set of real number zeros for your denominator is  , then you will have a vertical asymptote at   and so on up through  .
Horizontal asymptote:
If the degree of the numerator polynomial is less than the degree of the denominator polynomial, there is a horizontal asymptote at  , which is to say, the  -axis.
If the degree of the numerator polynomial is equal to the degree of the denominator polynomial, then there is a horizontal asymptote at  where  is the lead coefficient on the numerator polynomial and  is the lead coefficient on the denominaor polynomial.
If the degree of the numerator polynomial is greater than the degree of the denominator polynomial then there is no horizontal asymptote. If the difference in degree is 1, then there is a slant or oblique asymptote whose equation is equal to the result of polynomial long division of the numerator by the denominator excluding any remainder.
-intercept. Find the coordinate.
Set equal to the numerator polynomial. Substitute 0 for  , then solve for  , the -coordinate of the -intercept. The -intercept is the point )
-intercepts. Find all -coordinates of all -intercepts
Set the numerator polynomial equal to zero. Solve for all real-number zeros. Assume the set of real number zeros of the numerator polynomial is  . Then the -intercepts are the points: ,\,(\varphi_2,\,0)\ .\,.\,.\,(\varphi_n,\,0))
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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