Question

A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15.
Predict which statements are true about the intervals of the continuous function. Check all that apply.

f(x) > 0 over the interval (−, 3).
f(x) ≤ 0 over the interval [0, 2].
f(x) < 0 over the interval (−1, 1).
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ).

Answer 1

The true statements about the function are:

• f(x) ≤ 0 over the interval [0, 2].
• f(x)>0 over the interval (-2,0)
• f(x) ≥ 0 over the interval [2,∞)

How to determine the true statement?

The table of values is given as:

x     f(x)

-3    -15

-2     0

-1      3

0      0

1      -3

2      0

3      15

From the table, the function values do not exceed 0 at the interval 0 to 2.

This means that f(x) ≤ 0 over the interval [0, 2].

Also from the table, the function values exceeds 0 at the intervals greater than -2 but less than 0

This means that f(x)>0 over the interval (-2,0)

Also from the table, the function values are at least 0 at the intervals greater than 2

This means that f(x) ≥ 0 over the interval [2,∞)

Hence, the true statements are (b), (d) and (e)

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