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The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy

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Manager
Joined: 12 Jan 2015
Posts: 210
Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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03 Jun 2016, 09:18
Hi Bunuel / chetan2u,

I am not able to understand, how can you say that the graph move up 2 units up. I can see that in second equation there is "+2" but still how could you say.

If the equation would have been y = (x + 1)(x - 1)^2 - 2. Then will the graph will move 2 stps down..??

If the equation would have been x = (y + 1)(y - 1)^2 and some graph was given and we need to find the intercept of equation x = (y + 1)(y - 1)^2 + 2 or x = (y + 1)(y - 1)^2 -2. Then how will the graph move.

I have gone through the link math-coordinate-geometry-87652.html but it does not provide anything related to the movement of graph. Can you please provide basic understanding on the movement of graph so that if I come across any weired equation in exam I can make a rough idea of it.

I can't take this question lightly because its an official GMAT Prep question.

Thanks and Regards.
Prakhar
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Thanks and Regards,
Prakhar

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Joined: 02 Aug 2009
Posts: 6217
Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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03 Jun 2016, 09:51
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PrakharGMAT wrote:
Hi Bunuel / chetan2u,

I am not able to understand, how can you say that the graph move up 2 units up. I can see that in second equation there is "+2" but still how could you say.

If the equation would have been y = (x + 1)(x - 1)^2 - 2. Then will the graph will move 2 stps down..??

If the equation would have been x = (y + 1)(y - 1)^2 and some graph was given and we need to find the intercept of equation x = (y + 1)(y - 1)^2 + 2 or x = (y + 1)(y - 1)^2 -2. Then how will the graph move.

I have gone through the link math-coordinate-geometry-87652.html but it does not provide anything related to the movement of graph. Can you please provide basic understanding on the movement of graph so that if I come across any weired equation in exam I can make a rough idea of it.

I can't take this question lightly because its an official GMAT Prep question.

Thanks and Regards.
Prakhar

Hi,

let $$y = (x + 1)(x - 1)^2$$...
and $$y_1 = (x + 1)(x - 1)^2 +2 = y+2$$......

so when $$x= 0... y = (0+1)(0-1)^2 = 1$$ and $$y_1 = (0+1)(0-1)^2 + 2 = 1+2 = 3$$
when $$x=1... y = (1+1)(1-1)^2 = 0$$and $$y_1=0+2 = 2$$..

so for earlier existing values of y, $$y_1$$ is 2 more so the values of y has shifted two points up in new graph although the graph remains the same..

Quote:
If the equation would have been y = (x + 1)(x - 1)^2 - 2. Then will the graph will move 2 stps down..??

YES

$$x = (y + 1)(y - 1)^2$$and $$x_1 = (y + 1)(y - 1)^2 + 2$$.... the graph will move two steps right

DRAW the graph for all four and you will strengthen the concept on this

Hope it is clear
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Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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24 Sep 2016, 08:55
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There is a smart way to do these problems. I'd like to explain it for a few scenarios:

Let y = f(x) and lets assume f(x) as given in this question (f(x) = (x+1)(x-1)²)

Case 1: f(x) → f(x) + a
Move the graph of f(x) by a points in upward direction on the Y-axis, keeping its shape same

Case 2: f(x) → f(x) - a
Move the graph of f(x) by a points in downward direction on the Y-axis, keeping its shape same

Case 3: f(x) → f(x+a)
Move the graph of f(x) by a points in the left direction on the X-axis, keeping its shape same

Case 4: f(x) → f(x-a)
Move the graph of f(x) by a points in the right direction on the X-axis, keeping its shape same
(Yes, in case 3 and 4 the graph moves in opposite direction. If you have f(x+a) it moves to the left side(negative X-axis), and if it is f(x-a), it moves to right side(positive X-axis))

Case 5: f(x) → -f(x)
Take the image of f(x) in Y-axis as mirror

Case 6: f(x) → f(-x)
Turn the graph of f(x) by 180 degree about X-axis
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Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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25 Sep 2016, 11:09
y = (x + 1)(x - 1)^2 to y= (x+1)(x-1)^2 + 2 is equivalent to a "translation" of the whole graph 2 units upwards thus the y ordinates of the peaks and troughs ( max and min) points of the graph will shift 2 units upwards too ,
Manager
Joined: 23 Jan 2016
Posts: 213
Location: India
GPA: 3.2
Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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09 Oct 2016, 06:57
Hi Keats,

You have described well the various cases of graph movements, however could you please visually depict what -f(x) and f(-x) could look like? I am a little confused.

thank you,
Jon
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Joined: 05 Mar 2015
Posts: 980
Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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26 Oct 2016, 06:26
kapru wrote:
Bunuel
I am curious to know if question is twisted like

y = (x + 1)(x - 1)^2 in the xy-plane. At how many points does the graph ofy = (x + 1)(x - 1)^2 -2intercept the x-axis?

PS : I am looking for scenarios, where it can cut x axis more than once.

the graph(highlighted) will not cut x-axis at any point...
Intern
Joined: 28 Feb 2017
Posts: 6
Location: Pakistan
Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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03 Apr 2017, 07:33
This problem was so easy to just visualize the graph moving 2 units up and realizing that it would have only one solution. I missed the +2 in the equation which the question was asking and mistakenly answered C (Two points)
Manager
Joined: 26 Mar 2017
Posts: 145
Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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15 Jun 2017, 08:29
I guess the easiest questions I've ever encountered on the gmat

we just add a constant therefore we just shift up the graph by 2

You must be blind if you don't see that the shifted graph intersects the x-axis only once

cheers
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Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy [#permalink]

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14 Mar 2018, 19:30
Hi All,

Even though this graphing question looks complex, it's actually built on a real simple concept...

Graphing an equation is a fairly straightforward process when the equation is in "slope-intercept format" (e.g. y = mx + b); you plug in a value for X, do the calculation and get the value of Y, then graph the point (X,Y). Repeat as much as necessary.

Notice that the two given equations are almost identical? The only difference is that the second equation "adds 2" to the calculation. In the initial equation, you plug in a value for X and get a value for Y. In the second equation, you plug in the SAME value for X, but you have to "add 2" to the end result, so your Y is "2 greater" than before.

The effect of "adding 2" to Y means that the graph will look the same, but it will be "shifted up" 2 spots (since all of the values of Y will be 2 greater than they were before).

With the initial drawing, there are 2 X-intercepts. Shifting the entire graph "up" 2 spots will give us a picture with just 1 X-intercept.

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Re: The figure shows the graph of y = (x + 1)(x - 1)^2 in the xy   [#permalink] 14 Mar 2018, 19:30

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