## I am wondering if I am starting the curve sketching right

1. Sketch the curve

2. $\frac{x}{(x-1)^{2}}$

3. Here's what I have; the domain is all x except x ≠ 1, y-intercept of 0, x-intercept of 0, symmetric about the origin since it is an odd function, horizontal asymptote of 0, vertical asymptote of 1, and for the increasing and decreasing of the function, I'm wondering if I did it right. f'(x) = $\frac{1*(x-1)^{2}-x*2(x-1)*1}{(x-1)^{4}}$ = $\frac{(x-1)^{2}-2x(x-1)}{(x-1)^{4}}$ = after factoring out the one (x-1) $\frac{-x-1}{(x-1)^{3}}$ Increasing on (-1,1) and decreasing on (-∞,-1), (1,∞). There is no local maximum, because f(1) would result in division by 0 which is impossible. Local minimum of f(-1) = $\frac{-1}{4}$
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 Recognitions: Homework Help Science Advisor A lot of that is right. But it's certainly not an odd function and symmetric around the origin, is it? Some of the other stuff you've said would contradict that.

 Quote by Dick A lot of that is right. But it's certainly not an odd function and symmetric around the origin, is it? Some of the other stuff you've said would contradict that.
Based on using f(-x) would result in it being negative divided by positive which would make it an odd function, because it would be f(-x) = -f(x).

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## I am wondering if I am starting the curve sketching right

 Quote by frosty8688 Based on using f(-x) would result in it being negative divided by positive which would make it an odd function, because it would be f(-x) = -f(x).
f(1) is undefined. f(-1)=(-1/4) (as you said). That doesn't sound symmetric or odd to me.
(x-1)^2 is not an even function.
 So the answer would be neither odd or even and no symmetry.

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