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The graph of y= (-2x^3)/(x^3+5) has the same behavior as the graph of ________________?????

 Sep 10, 2016
 #1
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y= (-2x^3)/(x^3+5)

 

I assume that you are referring to the "end" behavior.

 

Since the higest power on x in both numerator and denominator is the same, the end behavior will be determined by the ratio of the coefficients on these highest powers.

 

So we have    y =  -2 / 1   = -2

 

Thus.......as x increases without bound in both directions, the function approaches  y = -2

 

Here's a graph that confirms this :  https://www.desmos.com/calculator/kcfoxqcmsf

 

 

 

cool cool cool

 Sep 10, 2016
 #2
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How could the graph of y=(-2x^3)/(x^2+5) possible have the same end behavior as the graph of y=-2???

 Sep 10, 2016
 #3
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Note that the question asks for  y= (-2x^3)/(x^3+5)  not  y= (-2x^3)/(x^2+5)........!!!!!

 

 

cool cool cool

 Sep 10, 2016

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