Exam 11: Polynomial and Rational Functions

If the function is written in the form , a ratio of polynomials, which of the following could be ?

One of the following tables of data comes from a linear function, one from an exponential function, and one from a power function. The formula for the power function is with a = _____ and b = _____.

George measures the force exerted by a certain spring when it is stretched various distances beyond its natural length. The data he gathers is compiled in the following table. - He wishes to describe the force as a function of the stretched distance, and decides to use a cubic function model. After fitting a cubic function to the data, he uses it to estimate the force when the spring is stretched 22 inches. What is his approximation (to three decimal places) of this force?

Determine the vertical and horizontal asymptotes, if they exist, of the function

Simplify , if possible.

The following figure gives the graphs of and . Which is smaller, a or b?

The formula for the exponential function shown in the following table is , where a = _____ and b = _____. Round both answers to 2 decimal places.

Which of the following could be a formula for the graph shown below?

The function Can be approximated by the function . On what interval do the two graphs look similar?

Let Satisfy the conditions , , and . Which of the following must be true?

What is the long-run behavior of the function

The following graphs are of functions of the form , where M and N are constants. Which graph has M > 0 and N < 0?

The graphs of and are shown in the figure below as viewed on the window [-10, 10] by [-25, 25]. What is the zero of ?

Which of the following are possible formulas for a fourth degree polynomial with at least one zero at , a double zero at , and long-run behavior: as .

A right circular cylinder has a volume of 126 cubic meters. The least possible surface area for the cylinder is approximately:

The following table represents the amount of monthly data handled by MichNet, the University of Michigan's gateway to the Internet, sampled at six month intervals for the years 1993-1995. (The data is from the Michigan Daily, March 30, 1996, p.4.) Let d be the number of data packets handled monthly (in billions), and t be time in years since December, 1992. Find equations for the best fit exponential function and the best fit power function that model these data (you do not have to enter your equations). By comparing their correlation coefficients, choose which model gives a better fit. A) The exponential model B) The power function model

Find the long-run behavior of the function .