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# The curve above is represented with which of the following equations?

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Math Expert
Joined: 02 Sep 2009
Posts: 59722
The curve above is represented with which of the following equations?  [#permalink]

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20 Oct 2019, 21:57
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Difficulty:

65% (hard)

Question Stats:

40% (01:49) correct 60% (02:01) wrong based on 45 sessions

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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) $$y=x^3+x$$

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Untitled.png [ 13.09 KiB | Viewed 521 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 8309
The curve above is represented with which of the following equations?  [#permalink]

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20 Oct 2019, 22:18
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1
Bunuel wrote:

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) $$y=x^3+x$$

Attachment:
Untitled.png

It cuts x axis at three places, so we should have THREE values of x at which y is 0, one negative, one near or 0 itself and one positive..
Check the choices..
(A) $$y=x^3-x^2=x^2(x-1)$$, so x=0 and 1..Only two values..Eliminate
(B) $$y=-x^3+x^2=x^2(1-x)$$, so x=0 and 1..Only two values..Eliminate
(C) $$y=-x^3+x=x(1-x^2)=x(1-x)(1+x)$$, so x=-1, 0 and 1..three values..possible
(D) $$y=x^3-x=x(x^2-1)=x(x-1)(1+x)$$, so x=-1, 0 and 1..three values..possible
(E) $$y=x^3+x$$.. Negative value NOT possible as x will never be 0

Between C and D, look at the coefficient of x^3..
If it is positive, it will sloping downwards on left and sloping upwards on right and vice versa..
So, here it should be positive..so x^3-x
You can also substitute values and see, say x= -2, then y=(-2)^3-(-2)=-6..True

D
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Joined: 23 Nov 2019
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Re: The curve above is represented with which of the following equations?  [#permalink]

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28 Nov 2019, 04:04
Why did we assume y to be negative. please help
Re: The curve above is represented with which of the following equations?   [#permalink] 28 Nov 2019, 04:04
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# The curve above is represented with which of the following equations?

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