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).

Question

Susan Sawyer

Mathematics

24 September, 07:14

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).

+3

Answers (1)

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Sonia Weiss · Answer 1

f (x) ≥ 0 over the interval [-1,1].

Step-by-step 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)