Question

Which is the graph of the function f(x) = x3 – x2 – 17x – 15?

Answer 1

Factor f(x) = x^3 − x^2 − 17x − 15:
f(x) = (x + 1)(x + 3)(x − 5).

So the x‑intercepts are x = −3, −1, 5 (all simple, so the graph crosses the x‑axis at each). The y‑intercept is f(0) = −15. End behavior: as x → −∞, f(x) → −∞; as x → +∞, f(x) → +∞.

Local extrema (from f'(x) = 3x^2 − 2x − 17):
- local max at x ≈ −2.070, f ≈ 7.03
- local min at x ≈ 2.737, f ≈ −48.52

So pick the cubic curve that crosses the x‑axis at −3, −1, 5, has y‑value −15 at x = 0, goes from −∞ on the left to +∞ on the right, and shows a small positive peak near x ≈ −2 and a deep negative valley near x ≈ 2.74.