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Chapter 1: Problem 109
Begin by graphing the cube root function, \(f(x)=\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$g(x)=\sqrt[3]{x+2}$$
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$$\text { Solve and check: } \frac{x-1}{5}-\frac{x+3}{2}=1-\frac{x}{4}$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. My graph of \((x-2)^{2}+(y+1)^{2}=16\) is my graph of \(x^{2}+y^{2}=16\) translated two units right and one unit down.
Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}(x-2)^{2}+(y+3)^{2} &=4 \\\y &=x-3\end{aligned}$$
A company that sells radios has yearly fixed costs of \(\$ 600,000 .\) It costs the company \(\$ 45\) to produce each radio. Each radio will sell for \(\$ 65 .\) The company's costs and revenue are modeled by the following functions, where \(x\) represents the number of radios produced and sold: \(C(x)=600,000+45 x\) This function models the company's costs. \(R(x)=65 x\) This function models the company's revenue. Find and interpret \((R-C)(20,000),(R-C)(30,000),\) and \((R-C)(40,000)\)
$$\text { Solve for } y: \quad x=y^{2}-1, y \geq 0$$
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