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phanikpk: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Fri Jun 06, 2014 11:48 pmFollowed by: 1 member

by phanikpk » Wed Jul 09, 2014 12:37 am

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Source: Beat The GMAT — Problem Solving | Wed Jul 09, 2014 12:37 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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)Â² 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)Â² + 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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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

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.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

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

https://graceeducation1613.wordpress.co ... questions/

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mcdesty: Master | Next Rank: 500 Posts; Posts: 116; Joined: Wed Mar 14, 2012 1:02 pmFollowed by: 11 members; Thanked: 20 times; GMAT Score:760

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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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Jul 11, 2014 10:10 am

Please find the Rules of Graph Shifting in File attached.

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Doc1.pdf: All Rules of Graph Shifting; (253.96 KiB) Downloaded 81 times

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