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by GMATGuruNY » Wed Jul 09, 2014 2:44 am
For any graph such that y = f(x):
y = f(x) + k moves the graph UP k places.
y = f(x) - k moves the graph DOWN k places.

In the problem above, the graph of y = (x+1)(x-1)² has an x-intercept to the left (at x=-1) and an x-intercept to the right (at x=1).
Adding 2 to the function -- yielding y = (x+1)(x-1)² + 2 -- will move the graph UP 2 places.
When the graph moves up 2 places, the intercept to the right will disappear, leaving only the x-intercept to the left.

The correct answer is B.
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by ceilidh.erickson » Wed Jul 09, 2014 7:23 am
Just to add to Mitch's explanation - don't worry if you don't know how to graph cubic functions! The GMAT doesn't actually require this knowledge. This question makes it seem like you need to know how a cubic function behaves, but what they're really testing is how functions in general move around on a graph when we add a constant.

Whenever you have a function:
y = _____ + 2
this will always looked the same as
y = _____
but the constant +2 indicates that we just shift up by two positions on the graph. They could give you a function with a completely unknowable formula, and it would behave the same way.
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by abhasjha » Wed Jul 09, 2014 11:06 pm
Hi,

Just wanted to share that the question involves knowledge of shifting , stretching and reflection of graph .although this question has not asked but you would do well to know if graph of f(x) is given and we are asked how the graph of f(x) - c would look like . here the graph will shift down c units down from the graph of f(x) ...

similarly what happens to graph f(x) if it is multiplied by c ; where c is greater than 1 . etc .

watch out this video on youtube where they have explained shifting, stretching and reflection of graph .
https://www.youtube.com/watch?v=5oQgzup9nx4
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by mcdesty » Thu Jul 10, 2014 10:06 am
See Img for shifting the graph of x^2. If you master these basics, the problem above should be a 10 second problem. After looking at the image graph:y=x^2-1, and y=x^2 - 2x + 1.
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by GMATinsight » Fri Jul 11, 2014 10:10 am
Please find the Rules of Graph Shifting in File attached.
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