SOLUTION: How do you graph 3x/ x^2+5x+4?

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Question 928592: How do you graph 3x/ x^2+5x+4?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
3x%2F%28+x%5E2%2B5x%2B4%29


Horizontal asymtptote for unbounded to the left and the right, of y=0, because degree of denominator is one more than degree of numerator.


Factor and look at critical points values.
%283x%29%2F%28%28x%2B1%29%28x%2B4%29%29
Critical values are -4, -1, 0.
Zero at x=0;
Vertical asymptotes at x=-4 and x=-1.


x%3C-4:
3%28neg%29%2F%28%28neg%29%28neg%29%29
3%2Aneg%2F%28pos%29
negative.

-4%3Cx%3C-1:
3%2Aneg%2F%28%28neg%29%28pos%29%29
positive


-1%3Cx%3C0:
3%2Aneg%2F%28%28pos%29%28pos%29%29
negative

0%3Cx:
positive.

Think about how the intervals should look, and then compare to the graph you would draw.......



graph%28300%2C300%2C+-8%2C5%2C-10%2C10%2C3x%2F%28+x%5E2%2B5x%2B4%29%29