How do you graph #f(x)=(x-2)/(x^2-5x-6)#?

1 Answer
Roy E.
Jan 28, 2017

Zero at #x=2#, vertical asympotes at #x=-1# and #x=+6#, horizontal asymptote #y=0#.

Explanation:

Quotient of two polynomials. The denominator has a degree less than the numerator (therefore there is one horizontal asympote #y=0#) and factorizes into #(x+1)(x-6)# which has no common factors with the numerator. Therefore there are exactly two asymptotes, #x==1# and #x=6#. There is clearly a zero when #x=2#.
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