The Cubing Function — Quiz

Question 24 • Algebraic Reasoning

Which is the graph of the function f of x is equal to x cubed plus 6 x squared plus 11 x plus 6 ?

Answer

Image with description On a coordinate plane, a curve goes through the point negative 6 comma negative 6. It intersects the x-axis at the point negative 5 comma 0 and increases to a relative maximum near negative 4.5 comma 0.4. Then it decreases to a relative minimum near negative 3.4 comma negative 0.4 and increases through the point negative 2 comma 6.

Image with description On a coordinate plane, a curve goes through the point negative 4 comma negative 8. It increases to a relative maximum near negative 2.5 comma negative 1.6. Then it decreases to a relative minimum near negative 1.4 comma negative 2.4,and increases through the point 0 comma 4.

Image with description On a coordinate plane, a curve goes through the point negative 4 comma negative 4. It intersects the x-axis at the point negative 3.5 comma 0 and increases to a relative maximum near negative 2.5 comma 2.4. Then it decreases to a relative minimum near negative 1.4 comma 1.8 and increases through the point 0 comma 8.

Image with description On a coordinate plane, a curve goes through the point negative 4 comma negative 6. It intersects the x-axis at the point negative 3 comma 0 and increases to a relative maximum near negative 2.5 comma 0.4. Then it decreases to a relative minimum near negative 1.4 comma negative 0.4 and increases through the point 0 comma 6.

Explanation

Factor the function: f(x) = (x + 1)(x + 2)(x + 3), so its x-intercepts are −1, −2, and −3. Also, f(0) = 6 and f(−4) = −6. Choice C matches these points and shows turning points near (−2.5, 0.4) and (−1.4, −0.4), consistent with the function’s shape.

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