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Chapter 1: Problem 97

Determine whether the statements use the word function in ways that are mathematically correct. Explain your reasoning. (a) The sales tax on a purchased item is a function of the selling price. (b) Your score on the next algebra exam is a function of the number of hours you study the night before the exam.

Short Answer

Expert verified
Statement (a) correctly uses the word 'function', while statement (b) does not.

Step by step solution

01

Understand Statement (a)

In the first statement, the selling price of the item is the input and the sales tax on the purchased item is the output. According to the laws regarding sales tax, each selling price corresponds to exactly one sales tax amount, which is a percentage of the selling price. Therefore, the sales tax on a purchased item is a function of the selling price.
02

Understand Statement (b)

In the second statement, the number of hours studied is the input, and the score on the exam is the output. Even though studying more might generally yield better scores, it's not guaranteed that studying for a given number of hours will lead to a specific score. Other factors like comprehension level, the difficulty of the exam, etc., may significantly affect the score, so multiple study hour values can correspond to the same score. Therefore, your score on the next algebra exam is not strictly a function of the number of hours you study the night before.
03

Conclusion

From the above analysis, statement (a) correctly uses the word 'function', because each selling price corresponds to exactly one sales tax amount. However, statement (b) does not use the term 'function' correctly, because a particular number of study hours can potentially lead to different exam scores, due to various other influencing factors.

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