91Ó°ÊÓ

Complete the following sentence: If weekly profit \(P\) is specified as a function of selling price \(s\), then the independent variable is \(\quad\) and the dependent variable is

What would happen to the price of a certain commodity if the demand was always greater than the supply? Illustrate with a demand and supply graph.

True or false? Every numerically specified function with domain \([0,10]\) can also be specified algebraically. Explain.

How do the graphs of two functions \(f(x)\) and \(g(x)\) differ if \(g(x)=f(x-5) ?\) (Try an example.)

Find a linear equation whose graph is the straight line with the given properties. Through \((p, q)\) and \((r, s)(p \neq r)\)

Sales figures show that your company sold 1,960 pen sets each week when they were priced at \(\$ 1 /\) pen set and 1,800 pen sets each week when they were priced at \(\$ 5 /\) pen set. What is the linear demand function for your pen sets? HINT [See Example 4.]

The production of ozone-layer damaging Freon 22 (chlorodifluoromethane) in developing countries rose from 200 tons in 2004 to a projected 590 tons in \(2010 .^{33}\) a. Use this information to find a linear model for the amount \(F\) of Freon 22 (in tons) as a function of time \(t\) in years since 2000 . b. Give the units of measurement and interpretation of the slope. c. Use the model from part (a) to estimate the 2008 figure and compare it with the actual projection of 400 tons.

In the Fahrenheit temperature scale, water freezes at \(32^{\circ} \mathrm{F}\) and boils at \(212^{\circ} \mathrm{F}\). In the Celsius scale, water freezes at \(0^{\circ} \mathrm{C}\) and boils at \(100^{\circ} \mathrm{C}\). Assuming that the Fahrenheit temperature \(F\) and the Celsius temperature \(C\) are related by a linear equation, find \(F\) in terms of \(C\). Use your equation to find the Fahrenheit temperatures corresponding to \(30^{\circ} \mathrm{C}, 22^{\circ} \mathrm{C},-10^{\circ} \mathrm{C}\), and \(-14^{\circ} \mathrm{C}\), to the nearest degree.

You have ascertained that a table of values of \(x\) and \(y\) corresponds to a linear function. How do you find an equation for that linear function?

Suppose that \(y\) is decreasing at a rate of 4 units per 3-unit increase of \(x\). What can we say about the slope of the linear relationship between \(x\) and \(y ?\) What can we say about the intercept?