SOLUTION: Gragh each function. Indicate with coordinate labels all x-interceptions, y-interceptions, maxima and minima. Indicate with a dotted line and label all vertical, horizontal, and ob

Question 855986: Gragh each function. Indicate with coordinate labels all x-interceptions, y-interceptions, maxima and minima. Indicate with a dotted line and label all vertical, horizontal, and oblique asymptotes.
f(x)=(x^3-4x^2+x+6) / (x^2 -3x+2)
Thank you for your help!
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
This will help most of the way, useful in sketching a graph.

Polynomial Division will show quotient of , so a slant asymptote will be , since the remainder, will become increasingly smaller as x becomes unbounded.

f(x) is factorable.

Numerator factored indicates zeros at x=-1 and x=3.
Hole at x=2. (see common factor in numerator and denominator).
Vertical Asymptote at x=1 (see what this does to denominator).
Slant asymptote, y=x+1.
You can test for signs around critical points -1,1,2,3.

Not sure why the hole at x=2 does not appear as a hole, but that IS a hole, undefined function at x=2.
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