Question

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, ∞).

Answer 1

To find which of the statements are true about the graphed functions, lets consider each statement.

• Since the function has 3 roots at -0.7, 0.76, 2.5, the value of function alternates between negative and positive values, whihc is clearly shown in the graph.

Consider first statement

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

• Consider a point x =  -1  which belongs to  (-∞, -0.7).
• Correspong F(-1)  = -1, from the graph.

• Also let x = 1, which belongs to (0.76, 2.5)

• F(1) is close to -1
• Therefore the statement is true

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

• From the reasoning in the first statement, its clear that this statement is false.

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

• Consider x = 0, belonging to  (-0.7, 0.76),
• F(0) = 2, which is >  0.
• Hence this statement is false

     

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

• Consider point x =0 , belongs to (-0.7, 0.76), F(0) = 2 >0
• Also consider x = 1.9, belongs to  (0.76, ∞)
• F(1.9) = -5.7 is given, which is less than 0.
• Hence the statement is false.

   

Answer 2

Answer:

the correct answer is option B