Which is a valid prediction about the continuous function f(x)?
Х
-3
-2
-1
0
1
2
f(x)
-15
-5
0
5
0
-5
Of(x) < 0 over the interval (-00, ).
Of(x) > 0 over the interval (-1, oo).
Of(x) > 0 over the interval [-1, 1).
Of(x) < 0 over the interval (0, 2).

The valid  prediction about the continuous function f(x) is:

             f(x) ≥ 0 over the interval [5, ∞).

Step-by-step explanation:

The table for f(x) is given by:

                 x         f(x)

                 -5         8

                 -3         4

                 -1          0

                  1          -2

                  3         -2

                  5          0

                  7          4

From the table of values of the function f(x) we see that the value of the function f(x) first decreases and then attains it minimum ( i.e. -2) and then increases continuously after x=5.

            Hence, the correct answer is:

                f(x) ≥ 0 over the interval [5, ∞).

(

f(x) ≤ 0 over the interval [–1, ∞).

This option is incorrect since the value of the function at x=5 is greater than zero.

f(x) > 0 over the interval (–∞, 1).

At x= =-1 we have f(x)=0 .

Hence, the option is incorrect.

f(x) < 0 over the interval (–∞. –1).

At x= -5 the value of f(x) is greater than zero.

Hence, this option is incorrect   )

77

step-by-step explanation: