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Chapter 3: Problem 45
Solve each rational inequality in Exercises \(43-60\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x+3}{x+4}<0 $$
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In Exercises 94鈥�97, use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function. $$f(x)=x^{3}+13 x^{2}+10 x-4$$
The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$ \frac{2}{x^{2}+3 x+2}-\frac{4}{x^{2}+4 x+3} $$
In Exercises 100鈥�103, determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm graphing a fourth-degree polynomial function with four turning points.
In Exercises \(98-99,\) use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. Then use the \([\mathrm{ZOOMOUT}]\) feature to show that \(f\) and \(g\) have identical end behavior. $$f(x)=-x^{4}+2 x^{3}-6 x, \quad g(x)=-x^{4}$$
Use a graphing utility to graph \(y=\frac{1}{x^{2}}, y=\frac{1}{x^{4}},\) and \(y=\frac{1}{x^{6}}\) in the same viewing rectangle. For even values of \(n,\) how does changing \(n\) affect the graph of \(y=\frac{1}{x^{n}} ?\)
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