SOLUTION: Rational Functions Graph and show all asymptotes and intercepts. a. x/x^2-4 b. 3/x^2-1 c. 2x+1/x+3 ASAP thanks

Algebra ->  Rational-functions -> SOLUTION: Rational Functions Graph and show all asymptotes and intercepts. a. x/x^2-4 b. 3/x^2-1 c. 2x+1/x+3 ASAP thanks       Log On


   

Question 194181: Rational Functions
Graph and show all asymptotes and intercepts.
a. x/x^2-4
b. 3/x^2-1
c. 2x+1/x+3
ASAP thanks
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Graph and show all asymptotes and intercepts.
a. x/(x^2-4)
Vertical asymptotes at x= -2 and at x = 2
Horizontal at y = 0x^2/x^2 = 0/1 = 0
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Comment: Horizontal asymptotes describe the behavior of the graph
when "x" becomes very large, positively or negatively.
In your problem x^2 will overwhelm all other terms.
You have no x^2 terms in the numerator so you
get y = 0x^2/1x^2 = 0/1 = 0 as the horizontal asymptote.
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%2F%28x%5E2-4%29%29
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b. 3/(x^2-1)
Vertical at x = -1 and at x = 1
Horizontal at y = 0
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Comment: Similarly, x^2 will overwhelm the fraction and approach zero
y = 0x^2/1x^2 = 0/1 = 0
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3%2F%28x%5E2-1%29%29
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c. 2x+1/x+3
Vertical at x = -3
Horizontal at y = 2x/x = 2/1 = 2
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The highest power of "x" is x
You have two in the numerator and one in the denominator.
You get y = 2x/x = 2 as the horizontal asymptote.
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%282x%2B1%29%2F%28x%2B3%29%29
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You should be able to see all these asymptotes in the graphs.
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Cheers,
Stan H.