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Chapter 2: Problem 8
Determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=x^{\frac{1}{3}}-4 x^{2}+7$$
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Use a graphing utility to graph \(y=\frac{1}{x}, y=\frac{1}{x^{3}},\) and \(\frac{1}{x^{5}}\) in the same viewing rectangle. For odd values of \(n,\) how does changing \(n\) affect the graph of \(y=\frac{1}{x^{n}} ?\)
Find the horizontal asymptote, if there is one, of the graph of rational function. $$f(x)=\frac{-2 x+1}{3 x+5}$$
Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$g(x)=\frac{1}{x+2}-2$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm solving a polynomial inequality that has a value for which the polynomial function is undefined.
What is a rational inequality?
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