91Ó°ÊÓ

Find all asymptotes, \(x\) -intercepts, and \(y\) -intercepts for the graph of each rational function and sketch the graph of the function. $$f(x)=\frac{x}{x^{2}+x-2}$$

Establish the best integral bounds for the roots of each equation according to the theorem on bounds. $$2 x^{3}-x^{2}-7 x+7=0$$

Find all asymptotes, \(x\) -intercepts, and \(y\) -intercepts for the graph of each rational function and sketch the graph of the function. $$f(x)=\frac{2}{x^{2}+1}$$

Find all asymptotes, \(x\) -intercepts, and \(y\) -intercepts for the graph of each rational function and sketch the graph of the function. $$f(x)=\frac{x}{x^{2}+1}$$

Establish the best integral bounds for the roots of each equation according to the theorem on bounds. $$x^{2}-7 x-16=0$$

Find all asymptotes, \(x\) -intercepts, and \(y\) -intercepts for the graph of each rational function and sketch the graph of the function. $$f(x)=\frac{x^{2}}{x+1}$$

Establish the best integral bounds for the roots of each equation according to the theorem on bounds. $$x^{2}+x-13=0$$

Find all asymptotes, \(x\) -intercepts, and \(y\) -intercepts for the graph of each rational function and sketch the graph of the function. $$f(x)=\frac{x^{2}}{x-1}$$

Solve each problem. Oscillating modulators. The number of oscillating modulators produced by a factory in \(t\) hours is given by the polynomial function \(n(t)=t^{2}+6 t\) for \(t \approx 1 .\) The cost in dollars of operating the factory for \(t\) hours is given by the function \(c(t)=36 t+500\) for \(t \geq 1 .\) The average cost per modulator is given by the rational function \(f(t)=\frac{36 t+500}{t^{2}+6 t}\) for \(t=1 .\) Graph the function \(f .\) What is the average cost per modulator at time \(t=20\) and time \(t=30 ?\) What can you conclude about the average cost per modulator after a long period of time?

We can find the zeros of a polynomial function by solving a polynomial equation. We can also work backward to find a polynomial function that has given zeros. a) Write a first-degree polynomial function whose zero is \(-2\) b) Write a second-degree polynomial function whose zeros are 5 and \(-5\) c) Write a third-degree polynomial function whose zeros are \(1,-3,\) and 4 d) Is there a polynomial function with any given number of zeros? What is its degree?