Which is a valid prediction about the continuous function f(x)? f(x) ≥ 0 over the interval [5, ∞). f(x) ≤ 0 over the interval [–1, ∞). f(x) > 0 over the interval (–∞, 1). f(x) < 0 over the interval (–∞. –1).

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

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

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, ∞).

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

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

Hence, the option is incorrect.

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

Hence, this option is incorrect   )

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