The Cubing Function — Quiz

Question 17 • Algebraic Reasoning

Which is the graph of the function f of x is equal to x cubed plus x squared plus 4 ?

Answer

Image with description On a coordinate plane, a curve goes through the point negative 4 comma negative 2. It increases to a relative maximum near negative 3 comma 2.3. Then it decreases to a relative minimum near negative 1.7 comma 2 and increases through the point negative 1 comma 6.

Image with description On a coordinate plane, a curve goes through the point negative 2 comma 2. It increases to a relative maximum near negative 1 comma 6.3. Then it decreases to a relative minimum near 0.3 comma 6 and increases through the point 1 comma 8.

Image with description On a coordinate plane, a curve goes through the point negative 2 comma negative 2. It increases to a relative maximum near negative 1 comma 2.3. Then it decreases to a relative minimum near 0.3 comma 2 and increases through the point 1 comma 6.

Image with description On a coordinate plane, a curve goes through the point negative 2 comma 0. It increases to a relative maximum near negative 1 comma 4.3. Then it decreases to a relative minimum near 0.3 comma 4 and increases through the point 1.5 comma 8.

Explanation

For f(x) = x³ + x² + 4, f(−2) = −8 + 4 + 4 = 0, and f(0) = 4. Its derivative is 3x² + 2x = x(3x + 2), so the graph has a local maximum at x = −2/3 and a local minimum at x = 0; both are near y = 4. Choice D matches these features, including the point (−2, 0).

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