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Chapter 2: Problem 41
Solve each polynomial inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$x^{3} \geq 9 x^{2}$$
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. The graph of this direct variation equation that has a positive constant of variation shows one variable increasing as the other variable decreases.
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.
You drive from your home to a vacation resort 600 miles away. You return on the same highway. The average velocity on the return trip is 10 miles per hour slower than the average velocity on the outgoing trip. Express the total time required to complete the round trip, \(T\), as a function of the average velocity on the outgoing trip, \(x .\)
Use everyday language to describe the behavior of a graph near its vertical asymptote if \(f(x) \rightarrow \infty\) as \(x \rightarrow-2^{-}\) and \(f(x) \rightarrow-\infty\) as \(x \rightarrow-2^{+}\).
Solve each inequality using a graphing utility. $$\frac{1}{x+1} \leq \frac{2}{x+4}$$
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