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Chapter 2: Problem 54
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x+4 y+16=0$$
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Will help you prepare for the material covered in the next section. Use a rectangular coordinate system to graph the circle with center \((1,-1)\) and radius 1.
Use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. In addition, graph the line \(y-x\) and visually determine if \(f\) and g are inverses. $$ f(x)=\sqrt[3]{x}-2, g(x)=(x+2)^{3} $$
Write a piecewise function that models each cellphone billing plan. Then graph the function. \(\$ 50\) per month buys 400 minutes. Additional time costs \(\$ 0.30\) per minute.
Here is the 2011 Federal Tax Rate Schedule \(X\) that specifies the tax owed by a single taxpayer. (TABLE CAN'T COPY) The preceding tax table can be modeled by a piecewise function, where \(x\) represents the taxable income of a single taxpayer and \(T(x)\) is the tax owed: $$T(x)=\left\\{\begin{array}{c}0.10 x \\\850.00+0.15(x-8500) \\\4750.00+0.25(x-34,500) \\\17,025.00+0.28(x-83,600) \\\\\frac{?}{?}\end{array}\right.$$ if \(\quad 0 < x \leq 8500\) if \(\quad 8500 < x \leq 34,500\) if \(\quad 34,500 < x \approx 83,600\) if \(\quad 83,600 < x =174,400\) if \(174,400 < x \leq 379,150\) if \(\quad x >379,150\). Use this information to solve. Find and interpret \(T(20,000)\)
Begin by graphing the standard cubic function, \(f(x)-x^{3} .\) Then use transformations of this graph to graph the given function. $$ h(x)-\frac{1}{2} x^{3} $$
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