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# The curve above is represented with which of the following

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The curve above is represented with which of the following [#permalink]  27 Jun 2008, 18:31
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74. The curve above is represented with which of the following equations?
(A) y=x^3-x^2
(B) y=-x^3+x^2
(C) y=-x^3+x
(D) y=x^3-x
(E) y=x^3+x

Peer
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Last edited by peergmatclub on 27 Jun 2008, 18:49, edited 1 time in total.
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Re: FM #74 PS Curves [#permalink]  27 Jun 2008, 18:43
Is there suppose to be a curve to go along with the question?
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Re: FM #74 PS Curves [#permalink]  27 Jun 2008, 18:50
Sorry i missed it in the original post
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Re: FM #74 PS Curves [#permalink]  28 Jun 2008, 03:50
Quote:
74. The curve above is represented with which of the following equations?
(A) y=x^3-x^2
(B) y=-x^3+x^2
(C) y=-x^3+x
(D) y=x^3-x
(E) y=x^3+x

When x tend to infinity, y>0 => B, C are out.

Now note that the equation f(x) = 0 that corresponds to the curve has three distinct roots.

And let’s consider the rest options:
(A) y=x^3-x^2 = x^2(x-1) – only two roots => out.
(D) y=x^3-x = x(x-1)(x+1) – three roots, just as we need. Keep it.
(E) y=x^3+x = x(x^2+1) – only one root => out.

Overall, D.
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Re: FM #74 PS Curves [#permalink]  28 Jun 2008, 07:35
Greenoak,

Thanks for ur respsonse.

I still did not understand how B & C are out.

Could you please explain in simple terms?

Peer
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Re: FM #74 PS Curves [#permalink]  28 Jun 2008, 07:46
can someone please post this as a jpeg..i cannot open the word doc...i get an error message..
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Re: FM #74 PS Curves [#permalink]  28 Jun 2008, 07:49
you can see that the function is asymmetrical f(-x) = -f(x) -> no x^2 -> A and B are out
it's supposed to be positive for large x -> C is out
for some positive values of x: f(x) < 0 -> E is out
D is correct
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Re: FM #74 PS Curves [#permalink]  28 Jun 2008, 07:52
Hi Peer,

Quote:
When x tend to infinity, y>0 => B, C are out.

In simple terms I mean this:

If x is large enough, x^3> x^2 and x^3>x. (Well, in general, if x>1, x^n>x^k for any n>=1 and k>=1 such as n>k) So, the sign of both -x^3+x^2 and -x^3+x will be negative. And in our graph, for large values of x, y is positive. This means than neither B nor C could correspond to the graph.

So basically this is it. Let me know if further explanation is necessary.
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Re: FM #74 PS Curves [#permalink]  29 Jun 2008, 08:06
Hi greenoak!
I did not understand one thing if this equation y=x^3-x represents this curve then for x=1 how the value of y is 0.
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Re: FM #74 PS Curves [#permalink]  29 Jun 2008, 10:36
Quote:
Hi greenoak!
I did not understand one thing if this equation y=x^3-x represents this curve then for x=1 how the value of y is 0.

Hello, value!

To say the truth, I don’t quite understand your question.

If f(x) = x^3-x, then f(1) = 1^3 – 1 = 0. But surely you couldn't mean this was not clear .

Or do you mean that from the graph, it is not clear that y=0 exactly for x=1 and not for some other x?

If so, let’s look at the graph. There are no numbers under the axis, so technically you are right and we cannot say – solely from the graph – what are the values of the roots (or the points of x-axis intercepts). However, we can say that there are three distinct roots: one is 0 and the other two are symmetrical relative to the y-axis. This condition, along with the fact that y>0 for large values of x, allows us to choose the only suitable answer. And, from the answer we have chosen (but not from the graph itself!), we can see that the roots are indeed 0, -1, 1.

However, if among the answer choices were something like y=x(x-2)(x+2) as well as y=x(x-1)(x+1), I think we could not have chosen between these two options – because the graph (which is not scaled) does not give us enough information to do so.

If I am mistaken about the intended meaning of your question – please, let me know; I'll try to explain better.
Re: FM #74 PS Curves   [#permalink] 29 Jun 2008, 10:36
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