Which best describes the graph of the cubic function f(x) = x3 + x2 + x + 1?

The function’s rate of change is given by its derivative: f′(x) = 3x² + 2x + 1. This quadratic is always positive because its discriminant is 2² − 4(3)(1) = −8, and it opens upward. So the graph increases as x increases everywhere, which matches choice A, “As x increases, y increases along the entire graph.”

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