Which best describes the graph of the cubic function f of x is equal to x cubed plus x squared plus x plus 1 ?

Differentiate the function: f′(x) = 3x² + 2x + 1. This derivative is always positive because its discriminant is 2² − 4(3)(1) = −8, so it has no real zeros, and the quadratic opens upward. Therefore, the function increases as x increases along its entire graph, which matches “As x increases, y increases along the entire graph.”

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