Question 22813: Rational Graphing
Can you please help with graphing f(x) = (x^2-6x) / (x-5)
Thank you
Answer by eclecticist(12)   (Show Source):
You can put this solution on YOUR website! The numerator can be simplified into x(x-6).
This means that there are two zeroes: one at 0 and one at 6.
From the denominator, you can see that there is a vertical asymptote at x-5, because when x = 5, the graph would be undefined.
Also, since the degree of the numerator is 2, and the degree of the degree of the denominator is 1, the degree of the numerator is one greater than the degree of the denominator, resulting in a slant/oblique asymptote. To find this asymptote, you would divide the numerator by the denominator and take the quotient only to find that the slant asymptote is x-1. The shape of the rest of the graph should then be obvious.
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