SOLUTION: Please please help!!!! h(x)=((x^2)(e^x))/x The function h is defined above. Which of the following are true about the graph of y=h(x)? -The graph has a vertical asymptote

Algebra ->  Rational-functions -> SOLUTION: Please please help!!!! h(x)=((x^2)(e^x))/x The function h is defined above. Which of the following are true about the graph of y=h(x)? -The graph has a vertical asymptote       Log On


   



Question 973447: Please please help!!!!
h(x)=((x^2)(e^x))/x
The function h is defined above. Which of the following are true about the graph of y=h(x)?
-The graph has a vertical asymptote at x=0
-The graph has a horizontal asymptote at y=0
-The graph has a minimum point
I know the minimum point is correct but the booklet is telling me that graph has a horizontal asymptote y=0 but I believe that is not true because for it to y=0 the denominator leading coefficient exponent value must be greater then the numerator value which is not the case unless I'm missing something. Thank you!!!

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h(x)=((x^2)(e^x))/x
The function h is defined above. Which of the following are true about the graph of y=h(x)?
-The graph has a vertical asymptote at x=0
-The graph has a horizontal asymptote at y=0
-The graph has a minimum point
I know the minimum point is correct but the booklet is telling me that graph has a horizontal asymptote y=0 but I believe that is not true because for it to y=0 the denominator leading coefficient exponent value must be greater then the numerator value which is not the case unless I'm missing something.
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No vertical asymptote.
It has a minimum @ x = -1
It has a horizontal asymptote y = 0.
As x increases in the negative direction, e^x approaches zero faster than x goes negative.
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x = 0 --> y = 0
x = -5 --> y = -0.0337
x = -10 --> y = -0.0005
x = -20 --> y = -4.1e-8
x = -30 --> y = -2.8e-12