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The figure shows the graphs of functions f and g, defin
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24 Feb 2022, 08:15
24 Feb 2022, 08:15
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Question Stats:
30% (00:57) correct
70% (02:38) wrong based on 10 sessions
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GRe The figure shows the.jpg [ 18.72 KiB | Viewed 2151 times ]
The figure shows the graphs of functions f and g, defined by \(f(x) = -x^3 + x\) and \(g(x) = f(x + m) + n\), where m and n are constants. What is \(m + n\)?
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The figure shows the graphs of functions f and g, defin
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Updated on: 31 Oct 2022, 08:08
Updated on: 31 Oct 2022, 08:08
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The given figure does not show an accurate graph for f(x) = -x^3 + x and thus does not seem viable.
Whereas the local minimum for f(x) = -x^3 + x is -2/(3√3) ≈ -0.38, the graph seems to show a local minimum near or at -1.
Also, coordinate plane in the figure is distorted in that the vertical distance between 0 and -1 seems much smaller than the horizontal distance between 0 and -1.
To avoid confusion, I would ignore the problem as written.
I believe that the following revision reflects the intent of the problem.
Screen Shot 2022-10-30 at 4.39.21 PM.png [ 144.08 KiB | Viewed 1248 times ]
The figure shows the graphs of f(x) and g(x), where g(x) = f(x + m) + n and m and n are constants. What is m + n?
Given any function f(x):
f(x) + 10 --> the graph shifts UP 10 places
f(x) - 10 --> the graph shifts DOWN 10 places
f(x-10) --> the graph shifts to the RIGHT 10 places
f(x+10) --> the graph shifts to the LEFT 10 places
Screen Shot 2022-10-30 at 4.41.49 PM.png [ 146.59 KiB | Viewed 1243 times ]
The red dot on f(x) moves up 1 place and to the left 2 places to become the green dot on g(x).
Since g(x) shifts the graph of f(x) up 1 place, n=1.
Since g(x) shifts the graph of f(x) to the left 2 places, m=2.
Thus:
m+n = 2 + 1 = 3
Whereas the local minimum for f(x) = -x^3 + x is -2/(3√3) ≈ -0.38, the graph seems to show a local minimum near or at -1.
Also, coordinate plane in the figure is distorted in that the vertical distance between 0 and -1 seems much smaller than the horizontal distance between 0 and -1.
To avoid confusion, I would ignore the problem as written.
I believe that the following revision reflects the intent of the problem.
Quote:
Attachment:
Screen Shot 2022-10-30 at 4.39.21 PM.png [ 144.08 KiB | Viewed 1248 times ]
The figure shows the graphs of f(x) and g(x), where g(x) = f(x + m) + n and m and n are constants. What is m + n?
Given any function f(x):
f(x) + 10 --> the graph shifts UP 10 places
f(x) - 10 --> the graph shifts DOWN 10 places
f(x-10) --> the graph shifts to the RIGHT 10 places
f(x+10) --> the graph shifts to the LEFT 10 places
Attachment:
Screen Shot 2022-10-30 at 4.41.49 PM.png [ 146.59 KiB | Viewed 1243 times ]
The red dot on f(x) moves up 1 place and to the left 2 places to become the green dot on g(x).
Since g(x) shifts the graph of f(x) up 1 place, n=1.
Since g(x) shifts the graph of f(x) to the left 2 places, m=2.
Thus:
m+n = 2 + 1 = 3
Originally posted by GMATGuruNY on 24 Feb 2022, 14:22.
Last edited by GMATGuruNY on 31 Oct 2022, 08:08, edited 3 times in total.
Last edited by GMATGuruNY on 31 Oct 2022, 08:08, edited 3 times in total.
General Discussion
Re: The figure shows the graphs of functions f and g, defin
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30 Oct 2022, 11:01
30 Oct 2022, 11:01
Hi the red dot in fact moves more then 2 places in x, doesnt it? since it starts out at -1 < x < 0 and ends up at -3.
