The curve above is represented with which of the following

Oldest

Best Reply

Author

Message

TAGS:

Intern

Joined: 27 Mar 2008

Posts: 25

Followers: 0

Kudos [?]: 0 [0], given: 0

The curve above is represented with which of the following [#permalink]

27 Jun 2008, 19:31

00:00

Question Stats:

0% (00:00) correct

0% (00:00) wrong

based on 0 sessions

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

Please helpe me how to approach these probelms

Peer

Attachments

graph.doc [26 KiB]
Downloaded 83 times

To download please login or register as a user

Last edited by peergmatclub on 27 Jun 2008, 19:49, edited 1 time in total.

Manager

Joined: 21 Mar 2008

Posts: 86

Followers: 1

Kudos [?]: 6 [0], given: 0

Re: FM #74 PS Curves [#permalink]

27 Jun 2008, 19:43

Is there suppose to be a curve to go along with the question?

Intern

Joined: 27 Mar 2008

Posts: 25

Followers: 0

Kudos [?]: 0 [0], given: 0

Re: FM #74 PS Curves [#permalink]

27 Jun 2008, 19:50

Sorry i missed it in the original post

Director

Joined: 12 Apr 2008

Posts: 501

Location: Eastern Europe

Schools: Oxford

Followers: 10

Kudos [?]: 129 [0], given: 4

Re: FM #74 PS Curves [#permalink]

28 Jun 2008, 04:50

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.

Intern

Joined: 27 Mar 2008

Posts: 25

Followers: 0

Kudos [?]: 0 [0], given: 0

Re: FM #74 PS Curves [#permalink]

28 Jun 2008, 08:35

Greenoak,

Thanks for ur respsonse.

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

Could you please explain in simple terms?

Peer

Current Student

Joined: 28 Dec 2004

Posts: 3439

Location: New York City

Schools: Wharton'11 HBS'12

Followers: 11

Kudos [?]: 134 [0], given: 2

Re: FM #74 PS Curves [#permalink]

28 Jun 2008, 08:46

can someone please post this as a jpeg..i cannot open the word doc...i get an error message..

Director

Joined: 01 Jan 2008

Posts: 635

Followers: 3

Kudos [?]: 114 [0], given: 1

Re: FM #74 PS Curves [#permalink]

28 Jun 2008, 08:49

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

Director

Joined: 12 Apr 2008

Posts: 501

Location: Eastern Europe

Schools: Oxford

Followers: 10

Kudos [?]: 129 [0], given: 4

Re: FM #74 PS Curves [#permalink]

28 Jun 2008, 08:52

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.

Manager

Joined: 13 Apr 2008

Posts: 66

Followers: 1

Kudos [?]: 3 [0], given: 0

Re: FM #74 PS Curves [#permalink]

29 Jun 2008, 09:06

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.

Director

Joined: 12 Apr 2008

Posts: 501

Location: Eastern Europe

Schools: Oxford

Followers: 10

Kudos [?]: 129 [0], given: 4

Re: FM #74 PS Curves [#permalink]

29 Jun 2008, 11:36

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, 11:36

		Similar topics	Author	Replies	Last post
Similar Topics:		represents the remainder of 3x/2, which of the following	Praetorian	7	12 Sep 2003, 04:04
		Which of the following equations represents a line that is	alimad	1	28 Sep 2006, 18:33
		Which of the following represents a logical flaw in the	sachint	1	30 Dec 2009, 09:57
	3	Which of the following represents the greatest value?	jamifahad	5	05 Jul 2011, 12:15
		In the coordinate system above, which of the following is	Walkabout	4	27 Dec 2012, 07:38

The curve above is represented with which of the following

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

The curve above is represented with which of the following

The curve above is represented with which of the following

Main navigation

GMAT Resources

Partners

MBA Resources