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 [ 2.27 KiB | Viewed 202 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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This is my response to the question and may be incorrect. Feel free to rectify any mistakes