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Chapter 3: Problem 94
Determine whether the statement is true or false. Justify your answer. The graph of a rational function can never cross one of its asymptotes.
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The annual profit \(P\) (in dollars) of a company is modeled by a function of the form \(P=a t^{2}+b t+c,\) where \(t\) represents the year. Discuss which of the following models the company might prefer. (a) \(a\) is positive and \(t \geq-b /(2 a)\) (b) \(a\) is positive and \(t \leq-b /(2 a)\) (c) \(a\) is negative and \(t \geq-b /(2 a)\) (d) \(a\) is negative and \(t \leq-b /(2 a)\)
(a) use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of \(f\) (b) list the possible rational zeros of \(f,\) (c) use a graphing utility to graph \(f\) so that some of the possible zeros in parts (a) and (b) can be disregarded, and (d) determine all the real zeros of \(f\). $$f(x)=4 x^{4}-17 x^{2}+4$$
Divide using long division. $$\left(2 x^{4}+x^{2}-11\right) \div\left(x^{2}+5\right)$$
Write the general form of the equation of the line that passes through the points. $$(3,2),(0,-1)$$
Use a graphing utility to graph the function and find its domain and range. $$f(x)=-x^{2}+9$$
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