Chapter 1: Q8E (page 7)
7-14 Determine whether the equation or table defines y as a function of x.
\({\bf{3}}{x^{\bf{2}}} - {\bf{2}}y = {\bf{5}}\)
The equation defines y as a function of x.
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If \(f\left( x \right) = x + \sqrt {{\bf{2}} - x} \) and \(g\left( u \right) = u + \sqrt {{\bf{2}} - u} \), is it true that \(f = g\)?
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window.
15-18 determine whether the curve is the graph of a function of \(x\). If it is, state the domain and range of the function.
15.
In this section we discussed examples of ordinary, everyday functions: population is a function of time, postage cost is a function of package weight, water temperature is a function of time. Give three other examples of functions from everyday life that are described verbally. What can you say about the domain and range of each of your functions? If possible, sketch a rough graph of each function.
Evaluate \(f\left( { - {\bf{3}}} \right)\), \(f\left( {\bf{0}} \right)\), and \(f\left( {\bf{2}} \right)\) for the piecewise defined function. Then sketch the graph of the function.
\(f\left( x \right) = \left\{ {\begin{aligned}{ - {\bf{1}}}&{{\bf{if}}\;\;x \le {\bf{1}}}\\{{\bf{7}} - {\bf{2}}x}&{{\bf{if}}\;\;x > {\bf{1}}}\end{aligned}} \right.\)
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