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On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).

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sqdancefan

Answer:

  (a)  F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Step-by-step explanation:

Wherever the function crosses the x-axis, its sign changes. This lets us make a map of the signs of the function, and identify intervals where it is positive and negative.

Sign changes

The x-intercepts are said to be at x ∈ {-0.7, 0.76, 2.5}.  These three crossing points divide the graph into four (4) intervals. The sign of the function is given as positive at x=0 and negative at x = 1.9. So, our sign map is ...

  < -0.7 . . . . . negative

  -0.7 to 0.76 . . . . . positive (2 at x=0, for example)

  0.76 to 2.5 . . . . . negative (-5.7 at 1.9, for example)

  > 2.5 . . . . . positive

Choosing from the descriptions, the one that matches is ...

  F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

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