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# For the function ((x)/(x-1)^2)) how do i know the graph increases towards the asymptotes instead of decreasing?

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my vertical asy is x= -1

my horiztonal asy is y=0

my intercepts are (1,0)

Thanks

Guest Apr 2, 2017
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f(x)  =  x / (x - 1)^2

This will have a horizontal asymptote at y = 0    the graph will approach this as it increases without bound both in a positive and negative direction

And it will will have a vertical asymptote at x  = 1

As x approaches 1 from both sides, y → infinity

To see this....pick some x values on either side of x = 1 that are increasingly closer and closer to 1 and evaluate them in the function.....here are some test values :

https://www.wolframalpha.com/input/?i=x+%2F+(x+-+1)%5E2++++for+x+%3D+.9,.99,+.999,.9999,+1.0001,+1.001,+1.01

Look  at the graph here : https://www.desmos.com/calculator/8yxvmnqor7

CPhill  Apr 2, 2017

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