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The figure above shows the graph of the function f defined

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Director
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Joined: 16 May 2014
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GRE 1: 326 Q165 V161
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The figure above shows the graph of the function f defined [#permalink] New post 29 May 2014, 02:05
Expert's post
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Attachment:
axis.jpg
axis.jpg [ 15.18 KiB | Viewed 19 times ]


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

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Last edited by Carcass on 29 Nov 2017, 12:12, edited 2 times in total.
Edited the question and added the OA
Director
Director
User avatar
Joined: 16 May 2014
Posts: 597
GRE 1: 326 Q165 V161
Followers: 72

Kudos [?]: 313 [0], given: 64

Re: Practice Question #3 [#permalink] New post 29 May 2014, 02:07
Expert's post

Explanation



You can see that all five choices are linear functions whose graphs are lines with various slopes and y-intercepts. The graph of Choice A is a line with slope 1 and y-intercept shown in the following figure
Attachment:
3s.JPG
3s.JPG [ 13.56 KiB | Viewed 1072 times ]


It is clear that this line will not intersect the graph of f to the left of the y-axis. To the right of the y-axis, the graph of f is a line with slope 2, which is greater than slope 1. Consequently, as the value of x increases, the value of y increases faster for f than for g, and therefore the graphs do not intersect to the right of the y-axis. Choice B is similarly ruled out. Note that if the y-intercept of either of the lines in choices A and B were greater than or equal to 4 instead of less than 4, they would intersect the graph of f.

Choices C and D are lines with slope 2 and y-intercepts less than 4. Hence, they are parallel to the graph of f (to the right of the y-axis) and therefore will not intersect it. Any line with a slope greater than 2 and a y-intercept less than 4, like the line in Choice E, will intersect the graph of f (to the right of the y-axis). The correct answer is Choice E.
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Re: Practice Question #3   [#permalink] 29 May 2014, 02:07
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The figure above shows the graph of the function f defined

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