SOLUTION: Explain how to Find any horizontal and vertical asymptotes and any holes that may exist for the rational function. Draw a graph, including any x and y intercepts: y=((x^2)+7x+1

Algebra ->  Rational-functions -> SOLUTION: Explain how to Find any horizontal and vertical asymptotes and any holes that may exist for the rational function. Draw a graph, including any x and y intercepts: y=((x^2)+7x+1      Log On


   

Question 895387: Explain how to Find any horizontal and vertical asymptotes and any holes that may exist for the rational function. Draw a graph, including any x and y intercepts:
y=((x^2)+7x+12)/(x+4)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
That rational equation has no horizontal asymptotes. Notice x unbounded approaches either negative infinity or positive infinity, based on y approaching x%5E2%2Fx.

Just to be more certain in possible vertical asymptotes, factorize the numerator if possible.
(x+3)(x+4)-----------the numerator.
NO vertical asymptote, because y=%28%28x%2B3%29%28x%2B4%29%29%2F%28x%2B4%29
y=%28%28x%2B3%29cross%28%28x%2B4%29%29%29%2Fcross%28%28x%2B4%29%29
y=x%2B3
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Your rational equation is the line but MISSING x=-4. There is no included point at x=-4. You can call this a hole in the line. (This cannot be seen well on most graphs produced through software, but you can represent what you want in a manually drawn graph or sketch.)

No real use in looking for slant asymptote, since the rational equation is already a line (missing one point.)