/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 107 (a) The sales tax on a purchased... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 107

(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
The scenario (a) is a function, whereas the scenario (b) is not generally considered a function.

Step by step solution

01

Determine if scenario (a) is a function

The sales tax on a purchased item is a function of the selling price. This is because for each unique selling price, there is exactly one calculated sales tax. Therefore, scenario (a) represents a function.
02

Determine if scenario (b) is a function

Although there is a clear relationship between studying and exam scores, it cannot be guaranteed that a specific number of study hours will result in a unique score because performance can also be affected by other factors such as understanding of the material, health condition, stress level etc. Hence, scenario (b) is generally not considered a function, because for a specific input (number of study hours), there may not be a unique output (exam score).

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Most popular questions from this chapter

In Exercises 39-54, (a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{x+1}{x-2} $$

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}\). $$ \begin{array}{cc} \text { Function } & x \text {-Values } \\ f(x)=-\sqrt{x+1}+3 &\quad x_{1}=3, x_{2}=8 \end{array} $$

(a) use the position equation \(s=-16 t^{2}+v_{0} t+s_{0}\) to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from \(t_{1}\) to \(t_{2}\), (d) interpret your answer to part (c) in the context of the problem, (e) find the equation of the secant line through \(t_{1}\) and \(t_{2}\), and (f) graph the secant line in the same viewing window as your position function. An object is thrown upward from ground level at a velocity of 120 feet per second. $$ t_{1}=3, t_{2}=5 $$

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}\). $$ \begin{array}{cc} \text { Function } & x \text {-Values } \\ f(x)=x^{3}-3 x^{2}-x &\quad x_{1}=1, x_{2}=3 \end{array} $$

True or False? In Exercises 85 and 86, determine whether the statement is true or false. Justify your answer. If the inverse function of \(f\) exists and the graph of \(f\) has a \(y\)-intercept, the \(y\)-intercept of \(f\) is an \(x\)-intercept of \(f^{-1}\).
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