Question

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).

Answer 1

The Answer here is A: f(x) ≥ 0 over the interval [5, ∞).

Explanation:

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Answer 2

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

f(x) ≥ 0 over the interval [5, ∞).

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 )