91Ó°ÊÓ

Find the slant asymptote of the graph of each rational function and \(\mathbf{b}\). Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$ f(x)=\frac{x^{2}+4}{x} $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with a fourth-degree polynomial function with integer coefficients and zeros at 1 and \(3+\sqrt{5} .\) I'm certain that \(3+\sqrt{2}\) cannot also be a zero of this function.

Explain why a polynomial function of degree 20 cannot cross the \(x\) -axis exactly once.

A company is planning to manufacture mountain bikes The fixed monthly cost will be \(\$ 100,000\) and it will cost \(\$ 100\) to produce each bicycle. a. Write the cost function, \(C\), of producing \(x\) mountain bikes. b. Write the average cost function, \(\bar{C},\) of producing \(x\) mountain bikes c. Find and interpret \(\bar{C}(500), \bar{C}(1000), \bar{C}(2000),\) and \(\bar{C}(4000)\) \- d. What is the horizontal asymptote for the graph of the average cost function, \(\bar{C}\) ? Describe what this means in practical terms.

A company that manufactures running shoes has a fixed monthly cost of \(\$ 300,000 .\) It costs \(\$ 30\) to produce each pair of shoes. a. Write the cost function, \(C\), of producing \(x\) pairs of shoes. b. Write the average cost function, \(\bar{C}\), of producing \(x\) pairs of shoes. c. Findandinterpret \(\bar{C}(1000), \bar{C}(10,000),\) and \(\bar{C}(100,000)\) d. What is the horizontal asymptote for the graph of the average cost function, \(\bar{C}\) ? Describe what this represents for the company.