Question

which statement is true about the graphed function f(x)?
f(x) < 0 over the intervals (-∞, -2.5) and (-0.75, 0.75)
f(x) > 0 over the intervals (-∞, -2.5) and (-0.75, 0.75)
f(x) < 0 over the intervals (-2.5, -0.75) and (-0.75, ∞)
f(x) > 0 over the intervals (-2.5, -0.75) and (0.75, ∞)

Explanation:

A function \( f(x) < 0 \) where its graph is below the x-axis, and \( f(x) > 0 \) where it is above. From the graph:

• \( f(x) > 0 \) over \( (-\infty, -2.5) \) (above x-axis left of -2.5) and \( (-0.75, 0.75) \) (above x-axis between -0.75 and 0.75).
• \( f(x) < 0 \) over \( (-2.5, -0.75) \) and \( (0.75, \infty) \) (below x-axis in these intervals).

Answer:

F(x) > 0 over the intervals (-∞, -2.5) and (-0.75, 0.75)