A Table of Selected Values for a Function Is Given

question 21

Multiple Choice

A table of selected values for a function is given. Also shown are tables of values for the derivative and the accumulation function with 0 as the starting point. Determine which table contains the values of the derivative, , and which contains the values of the accumulation function, . Justify your choice.

• A) Table 1 contains the values of because f is decreasing and the output values are negative. Table 2 contains the values of because its output is close to the cumulative sum of .
• B) Table 1 contains the values of because f is decreasing and the output values are negative. Table 2 contains the values of because cannot be negative.
• C) Table 1 contains the values of because its output is close to the cumulative sum of . Table 2 contains the values of because f is decreasing and the output values are negative.
• D) Table 1 contains the values of because the sign of the output does not change. Table 2 contains the values of because the output changes sign.
• E) Table 1 contains the values of because the magnitude of the output keeps increasing. Table 2 contains the values of because the output changes sign.

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Definitions:

Goal-Directed Behavior

Behavior motivated towards achieving a specific outcome or goal.

Overregularization

The tendency for young children to incorrectly use a regular grammar rule where they should use an exception to the rule.

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The process through which a person's ability to think, understand, and learn evolves over time.

Container

A general term for any object that can hold, store, or contain other objects or substances.