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Chapter 1: Problem 40
Use the algebraic tests to check for symmetry with respect to both axes and the origin. $$x y=4$$
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Data Analysis: Light Intensity A light probe is located \(x\) centimeters from a light source, and the intensity \(y\) (in microwatts per square centimeter) of the light is measured. The results are shown as ordered pairs \((x, y)\) (Spreadsheet at LarsonPrecalculus,com) $$\begin{array}{lll} (30,0.1881) & (34,0.1543) & (38,0.1172) \\ (42,0.0998) & (46,0.0775) & (50,0.0645) \end{array}$$ A model for the data is \(y=262.76 / x^{2.12}\) A. Use a graphing utility to plot the data points and the model in the same viewing window. B. Use the model to approximate the light intensity 25 centimeters from the light source.
Graph each of the functions with a graphing utility. Determine whether the function is even, odd, or neither. $$\begin{aligned}&\begin{array}{ll}f(x)=x^{2}-x^{4} & g(x)=2 x^{3}+1 \\\h(x)=x^{5}-2 x^{3}+x & j(x)=2-x^{6}-x^{8}\end{array}\\\&k(x)=x^{5}-2 x^{4}+x-2 \quad p(x)=x^{9}+3 x^{5}-x^{3}+x \end{aligned}$$
(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f(-3)=-8, \quad f(1)=2$$
(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f\left(\frac{2}{3}\right)=-\frac{15}{2}, \quad f(-4)=-11$$
The cost per unit in the production of an MP3 player is 60 dollars. The manufacturer charges 90 dollars per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by 0.15 dollars per MP3 player for each unit ordered in excess of 100 (for example, there would be a charge of 87 dollars per MP3 player for an order size of 120 ). (a) The table shows the profits \(P\) (in dollars) for various numbers of units ordered, \(x .\) Use the table to estimate the maximum profit. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Units, } x & 130 & 140 & 150 & 160 & 170 \\\\\hline \text { Profit, } P & 3315 & 3360 & 3375 & 3360 & 3315 \\\\\hline\end{array}$$ (b) Plot the points \((x, P)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(P\) as a function of \(x ?\) (c) Given that \(P\) is a function of \(x,\) write the function and determine its domain. (Note: \(P=R-C\) where \(R\) is revenue and \(C\) is cost.)
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