11
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Graphs of Polynomial Functions

Question 11 • [INMT3] Integrated Math 3 Sem 1 (26-27)

Which of the following statements are true about graphs of polynomial functions? Check all that apply.

Answer
A
The local maximum and local minimum always occur at a turning point.
B
The local maximum is the x-value of the coordinate at that point.
C
The ends of an even-degree polynomial either both approach positive infinity or both approach negative infinity.

Explanation

At a local maximum or minimum, the graph changes direction, so the extremum occurs at a turning point; statement A is true. A local maximum is the y-value at the point, not its x-value, so B is false. For an even-degree polynomial, both ends of the graph go in the same direction: they approach either positive infinity or negative infinity, making C true.

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