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

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The figure above shows the graph of the function f defined by [#permalink] New post 10 Sep 2017, 11:16
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75% (00:38) correct 25% (01:57) wrong based on 8 sessions
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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, f(x)
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

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Question: 3
Page: 118
Difficulty: medium
[Reveal] Spoiler: OA

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Re: The figure above shows the graph of the function f defined by [#permalink] New post 10 Sep 2017, 11:19
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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 −2. 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).

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Re: The figure above shows the graph of the function f defined by [#permalink] New post 02 Nov 2018, 12:52
I took it for a little more difficult problem, with f(g(x)) to be checked if intersecting the f(x) graph
Re: The figure above shows the graph of the function f defined by   [#permalink] 02 Nov 2018, 12:52
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The figure above shows the graph of the function f defined by

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