Question

A 2-column table with 8 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20.
Which could be the entire interval over which the function, f(x), is positive?

(–∞, 1)
(–2, 1)
(–∞, 0)
(1, 4)

Answer 1

(-2, 1)

Reason: f(-1)=2 and f(0)=2 (positive), while f(-2)=0 and f(1)=0 (zeros) and values outside (e.g. f(-3) and f(2)) are negative, so the only interval that could be entirely positive is (-2,1).