# Which statement is true about the graphed function f(x)?

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## 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, ∞).

F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75) ⇒ second answer

Step-by-step explanation:

* Lets explain the graph to answer the problem

– When we ask about f(x) we means the values of y

– f(x) > 0 means the graph is over the x-axis because over the x-axis

y is positive

– f(x) < 0 means the graph is under the x-axis because under the x-axis

y is negative

* Lets describe each part of the graph

– The graph intersect the x-axis at :

# x = -2.5 , x = -0.75 , x = 0 , x = 0.75

– The graph is over the x-axis between -∞ and -2.5 and between

-0.75 and 0.75

# At x = -2.5 f(x) = 0 , at x = -0.75 f(x) = 0 , at x = 0.75 f(x) = 0

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∴ x = (-∞ , -2.5) and (-0.75 , 0.75)

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

– The graph is under the x-axis between -2.5 and -0.75 and between

0.75 and ∞

∴ x = (-2.5 , -0.75) and (0.75 , ∞)

∴ f(x) < 0 over the intervals (-2.5 , -0.75) and (0.75 , ∞)

* The true statement in the answer is the second one:

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

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