91Ó°ÊÓ

Can the graph of a polynomial function have no y@intercept? Explain.

Find the axis of symmetry for each parabola whose equation is given. Use the axis of symmetry to find a second point on the parabola whose \(y\) -coordinate is the same as the given point. $$ f(x)=3(x+2)^{2}-5 ;(-1,-2) $$

Use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function. \(f(x)=-x^{5}+5 x^{4}-6 x^{3}+2 x+20\)

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 \( \text { of } f(x)=\frac{1}{x} \text { to graph } g \). $$ g(x)=\frac{3 x-7}{x-2} $$

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 \( \text { of } f(x)=\frac{1}{x} \text { to graph } g \). $$ g(x)=\frac{2 x-9}{x-4} $$

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. Find and interpret \(\bar{C}(1000), \bar{C}(10,000),\) and \(\bar{C}(100,000)\) D. What is the horizontal asymptote for the graph of the average cost function, \(\overrightarrow{\mathrm{C}}\) ? Describe what this represents for the company.

In Exercises 100–103, determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm graphing a fourth-degree polynomial function with four turning points.

There is more than one third-degree polynomial function with the same three x-intercepts.

Touches the x-axis at 0 and crosses the x-axis at 2; lies below the x-axis between 0 and 2

Exercises 113–115 will help you prepare for the material covered in the next section. Rewrite \(4-5 x-x^{2}+6 x^{3}\) in descending powers of \(x\)