2. 外语
  3. The figure above shows the graph of the function/defined by f(x)= \2x\ + 4 for all numbers x. For which of the following functio

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

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问题
The figure above shows the graph of the function/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?
选项 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
答案E
解析 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, shown in Figure 6.

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 /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, g(x)= 3x- 2.
This explanation uses the following strategies.
Strategy 3: Translate from an Algebraic to a Graphical Representation
Strategy 6: Add to a Geometric Figure
Strategy 8: Search for a Mathematical Relationship
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