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Which of the following is a possible equation for the above graph?
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10 Aug 2009, 20:11
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Which of the following is a possible equation for the above graph? A) x^3 B) x^3 1 C) 3x^3 + 2x D) 3x^3  2x E) x^3 + 3x^2  x + 2 Attachment:
Graph.png [ 11.02 KiB  Viewed 4361 times ]
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Re: Which of the following is a possible equation for the above graph?
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10 Aug 2009, 22:00
The graph is a plot of y=f(x) ,which we have to find. Look at the graph closely. The graph cuts at (0,0)
So when x=0, y =0 . This eliminates option B and E. When you substitute 0 in option B, y= x^3  1, if x=0 > y=0^3 1 =1. The corresponding coordinate is 0,1 which is not the case with the graph
When you substitute 0 in option E , y= x^3+3x^2x+2 , if x=0 y= 2. Again, the corresponding coordinate is 0,2 which is not the case.
Now we are left with options A,C and D.
In A, y =x^3. If x>0, y should be greater than 0. But this is not the case in the given graph. The graph has points in 4th quadrant which is (x,y). So option A can be ruled out.
Now consider C , y=3x^3 + 2x. Again if x>0 , y should be greater than 0. Ex. if x=1 , y= 5. if x=1/10 , y = 0.003+ 0.2 = 0.203. But this is not the case in the given graph. The graph has points in 4th quadrant which is (x,y). So option C can be ruled out.
Now consider D, y= 3x^3 2x , In this case , for x>0 , y can be gretaer than 0 or less than 0. For ex, if x=1/10, y= 0.003.02= 0.017. If x=1, y =1. For x=2, y=22. So for x> 0, Y can be less than or greater than 0, spanning I and IV quadrant. Therefore option D is correct.




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Re: Which of the following is a possible equation for the above graph?
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10 Aug 2009, 20:18
are we goin to use equation of line y=mx+b here?



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Re: Which of the following is a possible equation for the above graph?
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11 Aug 2009, 02:14
D it is I don't think we can use the slope formula here... its a simple case of solving for X or Y and seeing the corresponding points on the graph. What the source?
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Re: Which of the following is a possible equation for the above graph?
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11 Aug 2009, 03:14
Just use elimination, or substitution, when u sub in (0,0), u eliminate two choices, and when u sub in a small number, u elminate A and C. then u are left with D



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Re: Which of the following is a possible equation for the above graph?
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11 Aug 2009, 09:36
thank u 'Learner' for writing so much.Thanks a lot.(deserver a kudos) Sniper, source is Princeton prep course.



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Re: Which of the following is a possible equation for the above graph?
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23 May 2011, 21:30
well from the graph one can see three solutions  (0,0),(x,0) and (x,0).
substituting for y = f(x) we have,
C and D options left.
With a positive value for X, Y = 0 as can be seen in the positive half of the graph.
D is the only option left.



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Re: Which of the following is a possible equation for the above graph?
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23 Nov 2015, 10:28
Pretty sure calculus is not in the scope of the GMAT, so I apologize if this is a waste of time, but differentiation comes in handy here. There should be 2 points where the first derivative equals zero, i.e. a quadratic equation with 2 distinct roots for the local minima and maxima. This rules out A,B,and C. To decide between D and E, we apply second order conditions;we know that there is one inflection point at the origin, therefore the second derivative must = 0 where x = 0. For D, we have dy/dx = 9x^2  2; d2y/dx2 = 18x = 0, gives x=0, as required. Choose D. For E, we have dy/dx = 3x^2+6x1. d2y/dx2 = 6x+6 =0. x is not 0. The answer is D



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Re: Which of the following is a possible equation for the above graph?
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28 Dec 2015, 13:44
No need to know the equation of this scary graph.According to the graph, for x = 0. y = 0. This is possible in only three options. A,C and D For x^3, when x is positive, x^3 would never come below the x axis and give a negative value. Hence, A is discarded. From the other two options, take x as 0.5 and 1. Option D gives the negative dip.
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Re: Which of the following is a possible equation for the above graph?
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23 Sep 2017, 04:57
MohitRulz wrote: Which of the following is a possible equation for the above graph? A) x^3 B) x^3 1 C) 3x^3 + 2x D) 3x^3  2x E) x^3 + 3x^2  x + 2 Attachment: Graph.png The answer is D as follows. The graph shows that at x=0, y=0. Putting the value of x=0 in the above 5 equation will give that only A, C and D are left. B and E are out. Now we will have to calculate the slope. So using the concept of differentiation the formula for slope are as follows. A > 3\(x^2\) C > 9\(x^2\) + 2 D > 9\(x^2\)  2 From the graph we also know that the slope at x=0 is ve Putting the value of x=0 in the above 3 equations, we get A > 3\(0^2\) > 0 C > 9\(0^2\) + 2 > 2 D > 9\(0^2\)  2 > 2 Only D satisfied the required condition, Hence answer is D
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Which of the following is a possible equation for the above graph?
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25 Nov 2017, 13:10
A) x^3 B) x^3 1 C) 3x^3 + 2x D) 3x^3  2x E) x^3 + 3x^2  x + 2
one quick approach, i can think of,
First looking at the graph, there are up and downs, it means, there is no correlation between x and y. With this idea, let us attack the answer choices.
1.\(y = x^3\), when x is going to increase, y is also going to increase, there is corelation, so this can't be the equation 2. \(y = x^3 1\), when x is going to increase, y is also going to increase, there is corelation, so this can't be the equation. 3. \(y = 3x^3 + 2x\), when x is positive, y is also positive, when x is negative, y is also negative, no chance of up and down, so this can't be the equation.
So left which D and E.
We can eliminate one of them, by looking at graph, if x = 0, then y = 0, only choice D satisfies.
That should be our answer (D)



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Which of the following is a possible equation for the above graph?
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19 Feb 2019, 13:24
Since the graph passes through (0, 0), the correct answer must yield y=0 when x=0. Eliminate B and E, which do NOT yield y=0 when x=0. The graph has three xintercepts. Eliminate any remaining answer that will not yield three xintercepts. Since A will yield an xintercept only at (0, 0), eliminate A. Calculate the xintercepts for C: \(0 = 3x^3 + 2x\) \(0 = x(3x^2 + 2)\) \(x=0\) or \(x^2 = \frac{2}{3}\) Since \(x^2 = \frac{2}{3}\) has no real solutions, C will yield an xintercept only at (0, 0). Eliminate C.
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Which of the following is a possible equation for the above graph?
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19 Feb 2019, 13:24






