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Chapter 3: Problem 5
Determine which functions are polynomial functions. For those that are, identify the degree. $$h(x)=7 x^{3}+2 x^{2}+\frac{1}{x}$$
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Write an equation that expresses each relationship. Then solve the equation for \(y .\) \(x\) varies directly as \(z\) and inversely as the sum of \(y\) and \(w\).
Will help you prepare for the material covered in the next section. a. If \(y=\frac{k}{x},\) find the value of \(k\) using \(x=8\) and \(y=12\) b. Substitute the value for \(k\) into \(y=\frac{k}{x}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=3\)
Determine whether each statement makes sense or does not make sense, and explain your reasoning. When all is said and done, it seems to me that direct variation equations are special kinds of linear functions and inverse variation equations are special kinds of rational functions.
Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies jointly as \(a\) and \(b\) and inversely as the square root of \(c . y=12\) when \(a=3, b=2,\) and \(c=25 .\) Find \(y\) when \(a=5, b=3,\) and \(c=9\).
If you are given the equation of a rational function, how can you tell if the graph has a slant asymptote? If it does, how do you find its equation?
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