Answer:
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
∴ 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 ∞
# At x = -2.5 f(x) = 0 , at x = -0.75 f(x) = 0 , at x = 0.75 f(x) = 0
∴ 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).
