Practice Exam

Question 15 • Algebraic Reasoning

Which is the graph of the function f of x is equal to x cubed minus x squared minus 17 x minus 15 ?

Answer

Image with description On a coordinate plane, a curve goes through the point negative 3.5 comma 0. It increases to a relative maximum near negative 2 comma 12. Then it decreases to a relative minimum near 2.5 comma negative 40 and increases through the point 4.8 comma 0.

Image with description On a coordinate plane, a curve goes through the point negative 4 comma 0. It increases to a relative maximum near negative 2 comma 35. Then it decreases to a relative minimum near 2.5 comma negative 18 and increases through the point 4 comma 0.

Image with description On a coordinate plane, a curve goes through the point negative 4 comma 0. It increases to a relative maximum near negative 2 comma 22. Then it decreases to a relative minimum near 2.5 comma negative 28 and increases through the point 4.5 comma 0.

Image with description On a coordinate plane, a curve goes through the point negative 3 comma 0. It increases to a relative maximum near negative 2 comma 12. Then it decreases to a relative minimum near 2.5 comma negative 48 and increases through the point 5 comma 0.

Explanation

Factor the polynomial: x³ − x² − 17x − 15 = (x + 3)(x + 1)(x − 5), so its x-intercepts are −3, −1, and 5. The graph in choice D has the matching outer intercepts at −3 and 5 and the matching deep minimum (about −48). Its middle intercept at −1 is not mentioned in the description, but it lies between the two turning points.

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