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Chapter 1: Problem 13
Determine whether the equation represents \(y\) as a function of \(x .\) $$2 x+3 y=4$$
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For groups of 80 or more people, a charter bus company determines the rate per person according to the formula Rate \(=8-0.05(n-80), \quad n \geq 80\) where the rate is given in dollars and \(n\) is the number of people. (a) Write the revenue \(R\) for the bus company as a function of \(n\) (b) Use the function in part (a) to complete the table. What can you conclude? $$\begin{array}{|l|l|l|l|l|l|l|l|}\hline n & 90 & 100 & 110 & 120 & 130 & 140 & 150 \\\\\hline R(n) & & & & & & & \\\\\hline\end{array}$$
Sketch the graph of the function. $$f(x)=\left\\{\begin{array}{ll}\sqrt{4+x}, & x<0 \\\\\sqrt{4-x}, & x \geq 0\end{array}\right.$$
Sketch the graph of the function. $$g(x)=-[[x]]$$
The diameter of the largest particle that can be moved by a stream varies approximately directly as the square of the velocity of the stream. A stream with a velocity of \(\frac{1}{4}\) mile per hour can move coarse sand particles about 0.02 inch in diameter. Approximate the velocity required to carry particles 0.12 inch in diameter.
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.
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