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Chapter 3: Problem 91
Solve each inequality in Exercises \(86-91\) using a graphing utility. $$ \frac{1}{x+1} \leq \frac{2}{x+4} $$
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Use long division to rewrite the equation for \(g\) in the form $$ \text {quotient}+\frac{\text {remainder}}{\text {divisor}} $$ Then use this form of the function's equation and transformations \( \text { of } f(x)=\frac{1}{x} \text { to graph } g \). $$ g(x)=\frac{2 x-9}{x-4} $$
In Exercises 41鈥�64, a. Use the Leading Coefficient Test to determine the graph鈥檚 end behavior. b. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. c. Find the y-intercept. d. Determine whether the graph has y-axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly. $$f(x)=-3 x^{3}(x-1)^{2}(x+3)$$
Will help you prepare for the material covered in the next section. $$ \text { Solve: } x^{3}+x^{2}=4 x+4 $$
In Exercises 94鈥�97, use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function. $$f(x)=-x^{5}+5 x^{4}-6 x^{3}+2 x+20$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. As production level increases, the average cost for a company to produce each unit of its product also increases.
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