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The figure above shows the graph of the function defined by

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Intern
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The figure above shows the graph of the function defined by [#permalink] New post 24 Jan 2019, 20:55
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100% (00:15) correct 0% (00:00) wrong based on 2 sessions
Please can anyone help with this question, the correct choice is E, how can we solve such questions.
Please look at the attached image.
thnxxxx

Attachment:
#GREpracticequestion The figure above shows the graph of the ftmctionf defined by.jpg
#GREpracticequestion The figure above shows the graph of the ftmctionf defined by.jpg [ 12.85 KiB | Viewed 222 times ]


The figure above shows the graph of the function defined by \(f(x) = |2x| +4\) for all numbers x. For which of the following function g defined for all numbers x does the graph of g intersect the graph of \(f\) ?

A. \(g(x)=x — 2\)

B. \(g(x)=x + 3\)

C. \(g(x)= 2x — 2\)

D. \(g(x) = 2x + 3\)

E. \(g(x) = 3x — 2\)
[Reveal] Spoiler: OA

Last edited by amorphous on 26 Jan 2019, 17:45, edited 5 times in total.
Edited by Carcass
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Re: The figure above shows the graph of the function defined by [#permalink] New post 26 Jan 2019, 18:00
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This is one of the sample question by ETS available in their website.

Here the main point to remember is sometimes you need to draw the figure to find the right answer.
First of all notice that the given eqn of the line has a slope of 2, option C and D also have a slope of 2 so we can put a value for x and see if any of the two lines will intersect the given eqn for \(f(x)\).
Let us take \(x = 1\) we get, for c: \(g(x) = 0\); for D: \(g(x) = 5\)\(\)
Since C and D do not intersect \(f(x)\) for \(x = 1\) we can conclude they will not intersect f(x) because f(x) and g(x) have the same slope.

option \(A\)and \(B\) are linear graph.

Let us draw the figure for option A in a graph
Attachment:
intersection.gif
intersection.gif [ 2.27 KiB | Viewed 207 times ]

This graph will not intersect line f(x) this is because slope of line f(x) is 2 whereas the slope of line g(x) is 1. For every increase in value of x f(x) will be more steeper than g(x). Choice B can be eliminated as well. This leaves us with choice E only.
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Re: The figure above shows the graph of the function defined by [#permalink] New post 27 Jan 2019, 11:51
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The question is discussed here

https://greprepclub.com/forum/the-gure- ... -6322.html

Do a search on the board before to post a question. Especially if they are official question. We discussed all of them here on the board

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Re: The figure above shows the graph of the function defined by   [#permalink] 27 Jan 2019, 11:51
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