Question

The function, f(x), is a third-degree polynomial whose zeros are shown on the number line. Use the function values below to determine the solutions set of f(x) ≤ 0.



f(–3) = –15

f(–1) = 3

f(1) = –3

f(3) = 15

Which intervals are in the solution set of f(x) ≤ 0? Check all that apply.

(–∞, –2]
[–2, 0]
[–2, 2]
[0, 2]
[0, ∞)
[2, ∞)

Answer 1

The zeros are at x = −2, 0, 2. Using the given values:
- f(−3) < 0 so f < 0 on (−∞, −2),
- f(−1) > 0 so f > 0 on (−2, 0),
- f(1) < 0 so f < 0 on (0, 2),
- f(3) > 0 so f > 0 on (2, ∞).

Including the zeros (f = 0) gives the solution set (−∞, −2] ∪ [0, 2].

So check: (−∞, −2] and [0, 2].