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# The figure above shows the graph of the function f defined

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The figure above shows the graph of the function f defined [#permalink]  29 May 2014, 02:05
Expert's post
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Question Stats:

66% (00:58) correct 33% (01:28) wrong based on 3 sessions
Attachment:

axis.jpg [ 15.18 KiB | Viewed 543 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
Joined: 16 May 2014
Posts: 596
GRE 1: Q165 V161
Followers: 85

Kudos [?]: 398 [0], given: 64

Re: Practice Question #3 [#permalink]  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 [ 13.56 KiB | Viewed 1597 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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