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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (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 x%2B1%2B%282x%2B4%29%2F%28x%5E2-3x%2B2%29, so a slant asymptote will be highlight%28y=x%2B1%29, since the remainder, %282x%2B4%29%2F%28x%5E2-3x%2B2%29 will become increasingly smaller as x becomes unbounded.

f(x) is factorable.
highlight_green%28f%28x%29=%28%28x%2B1%29%28x-2%29%28x-3%29%29%2F%28%28x-1%29%28x-2%29%29%29

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.

graph%28300%2C300%2C-3%2C6%2C-10%2C15%2C%28x%5E3-4x%5E2%2Bx%2B6%29%2F%28x%5E2-3x%2B2%29%29
Not sure why the hole at x=2 does not appear as a hole, but that IS a hole, undefined function at x=2.