Question 200012: Given the rational function f(x)=x^2+2x/2x^2-x A) Write the function in factored form and then simplify. B)Find the domain (refer to the factored form before the function was simplified).C) Find the equation for each vertical and horizontal asymptote,if there us any. D)Find the range. E)Find any intercepts... Once again if you could show allof the allgabric work you did to find the solutions A-E it woulb be a great help to me so THANK YOU ONCE AGAIN
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! y= [x^2 +2x] / [2x^2 -x] = [ x (x+2)] / [ x(2x-1) ] = (x+2) /(2x-1)
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Hole @ x=0,,,,,,due to cancelling x in num and dem
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Vertical Asymptote @ x=1/2,,,,from den (2x-1) =0
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Horizontal Asymptote @ y=0, ,,,,,from degree of num and den equal
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x intercepts, zeros of den,,,x=0,,,x= -2,,,,,from (x+2)=0
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DOMAIN is all REAL Numbers, except hole at x=0,,and asymptote at x=1/2
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a rough sketch of the function would be helpful.
Starting at the far left, y =.5, curves downward to (-2,0) and the further down to
pass thru hole at (0,-2), and then still further downward to asymptote at x=1/2.
On the positive side of the asymptote, y is at positive infinity, curving down to the
horizontal asymptote at y=0.
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the RANGE is all real numbers except, asymptote at y= 0, and the hole at (0,-2)
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