Question

A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 15, negative 5, 0, 5, 0, negative 5.

Which is a valid prediction about the continuous function f(x)?

f(x) ≤ 0 over the interval (–∞, ∞).
f(x) > 0 over the interval (–1, ∞).
f(x) ≥ 0 over the interval [–1, 1].
f(x) < 0 over the interval (0, 2).

Answer 1

Explanation:

Answer:

f(x) ≥ 0 over the interval [-1,1].

Explanation:

The ordered pairs of the given function in table are (-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

It is clear from the values of f(x) with respect to x, that the function reaches zero at x = -1, then goes up to 5 at x = 0 and then again reaches zero at x = 1.

Hence, the value of f(x) remains positive within the interval of [-1,1].

Hence, we can write f(x) ≥ 0 over the interval [-1,1]. (Answer)

Answer 2

f(x) ≥ 0 over the interval [-1,1].

Explanation:

The ordered pairs of the given function in table are (-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

It is clear from the values of f(x) with respect to x, that the function reaches zero at x = -1, then goes up to 5 at x = 0 and then again reaches zero at x = 1.

Hence, the value of f(x) remains positive within the interval of [-1,1].

Hence, we can write f(x) ≥ 0 over the interval [-1,1]. (Answer)