91Ó°ÊÓ

Yes or No? If No, give a reason. (a) Can the average rate of change of an increasing function ever be negative? (b) If the average rate of change of a function between \(x=a\) and \(x=b\) is negative, then is the function necessarily decreasing on the interval \((a, b) ?\)

A function \(f\) is given. (a) Sketch a graph of \(f .\) (b) Use the graph to find the domain and range of \(f\). $$f(x)=x-2, \quad-2 \leq x \leq 5$$

Linear Functions Given Numerically A table of values for a linear function \(f\) is given. (a) Find the rate of change of \(f\) (b) Express \(f\) in the form \(f(x)=a x+b\) $$\begin{array}{|c|c|}\hline x & f(x) \\\\\hline 0 & 7 \\\2 & 10 \\\4 & 13 \\\6 & 16 \\\8 & 19 \\\\\hline\end{array}$$

The table shows the number of DVD players sold in a small electronics store in the years 2003-2013. $$\begin{array}{|c|c|} \hline \text { Year } & \text { DVD players sold } \\ \hline 2003 & 495 \\ 2004 & 513 \\ 2005 & 410 \\ 2006 & 402 \\ 2007 & 520 \\ 2008 & 580 \\ 2009 & 631 \\ 2010 & 719 \\ 2011 & 624 \\ 2012 & 582 \\ 2013 & 635 \\ \hline \end{array}$$ (a) What was the average rate of change of sales between 2003 and 2013 ? (b) What was the average rate of change of sales between 2003 and 2004 ? (c) What was the average rate of change of sales between 2004 and 2005 ? (d) Between which two successive years did DVD player sales increase most quickly? Decrease most quickly?

Use the Inverse Function Property to show that \(f\) and \(g\) are inverses of each other. $$f(x)=3 x+4 ; \quad g(x)=\frac{x-4}{3}$$

Find the domain and range of the function. $$f(x)=3 x, \quad-2 \leq x \leq 6$$

A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of \(2 \mathrm{cm} / \mathrm{s} .\) Express the surface area of the balloon as a function of time \(t\) (in seconds).

Taxicab Function \(\quad\) A taxi company charges \(\$ 2.00\) for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost \(C\) (in dollars) of a ride as a piecewise defined function of the distance \(x\) traveled (in miles) for \(0 < x < 2,\) and sketch a graph of this function.