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Qualitative Behavior of Graphs and Functions

In this rather vague category, you will be asked how a function and its graph are related. You may be asked to identify the zeros of a function based on its graph. The zeros, or roots, of a function are the x-coordinates of where it crosses the x-axis. Or you may be given two graphs and asked for what x values are their functions equal. The functions will be equal where they intersect.

The graphs of y = f(x) and y = 1 are shown to the right. For how many x values does f(x) equal 1?

  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

The figure shows that the graphs intersect at three points.


At each of these points, both graphs have a height, or y-coordinate, of 1.


The points are approximately (–.8, 1), (1.2, 1), and (4, 1).


Hence, f(x) = 1 for three x values.


The answer is (D).

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