3
QuizMultiple Choice

Cubic and Cube Root Functions — Test

Question 3 • Algebraic Reasoning

Which statements correctly describe the graph of the function f of x is equal to x cubed minus 2 x squared minus 19 x plus 20 ? Choose three correct answers.

Answer
A
The range of the function is y is greater than or equal to 20 .
B
As x approaches negative infinity, y approaches negative infinity.
C
The domain of the function is all real numbers.
D
The graph has a positive y -intercept.
E
As the x -values increase, the y -values always increase.

Explanation

The y-intercept is f(0) = 20, which is positive, so A is correct. Since f is a polynomial, its domain is all real numbers, making B correct. Its leading term is x³, so as x approaches negative infinity, the function also approaches negative infinity; C is correct. D is false because the function does not always increase, and E is false because a cubic with positive leading coefficient has a range of all real numbers.

AI-written and checked against the verified answer.

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