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Chapter 3: Problem 103
Write a rational inequality whose solution set is \((-\infty,-4) \cup[3, \infty)\).
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Write the equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degreeof \(p\) and \(q\) are as small as possible. More than one correct finction may be possible. Graph your function using a graphing utility to verify that it has the required propertics \(f\) has vertical asymptotes given by \(x=-2\) and \(x=2\) a horizontal asymptote \(y=2, y\) -intercept at \(\frac{9}{2}, x\) -intercepts at \(-3\) and \(3,\) and \(y\) -axis symmetry.
Write an equation that expresses each relationship. Then solve the equation for \(y .\) \(x\) varies directly as \(z\) and inversely as the difference between \(y\) and \(w\).
Describe how to graph a rational function.
The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the voltage remains constant, what needs to be done to triple the amount of heat generated?
If \(f\) is a polynomial or rational function, explain how the graph of \(f\) can be used to visualize the solution set of the inequality \(f(x)<0\).
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