Exam 11: Polynomial and Rational Functions

Suppose that a, b, c, and d are integers and that a is positive and even, b is positive and odd, c is negative and even, and d is negative and odd. Which of the following graphs could correspond to the power function ? If none of the graphs correspond to the function, enter "none".C

The figure below shows the graphs of two power functions, f and g. The formula for g is , where k = _____ and p = _____.

Let be a polynomial of degree 5. Let be a polynomial of degree 4. Which of the following are true about ?

A 14 kg sample of a certain alloy (mixture of metals) contains 5 kg of tin and 9 kg of copper. A chemist decides to study the properties of the alloy as its percentage of tin is varied. Suppose x represents the quantity of tin, in kg, the chemist adds to the sample. Let represent the fraction of the mixture's mass composed of tin--that is, the ratio of the tin's mass to the mixture's total mass. A negative value of x represents a quantity of tin removed from the original 14 kg sample. = ______ kg. Round to 2 decimal places.

The following figure gives the graphs of and . If , what is a?

One of the following tables of data comes from a linear function, one from an exponential function, and one from a power function. Which one is the power function?

Find a power function through the two points( 2, 512)and (5,125000) .

A 16 kg sample of a certain alloy (mixture of metals) contains 4 kg of tin and 12 kg of copper. A chemist decides to study the properties of the alloy as its percentage of tin is varied. Suppose x represents the quantity of tin, in kg, the chemist adds to the sample. Let represent the fraction of the mixture's mass composed of tin--that is, the ratio of the tin's mass to the mixture's total mass. A negative value of x represents a quantity of tin removed from the original 16 kg sample . = ______ (kg tin)/(kg mixture). Round to 2 decimal places.

Is a rational function?

The following table represents the amount of monthly data handled by an Internet server, sampled at six month intervals for the years 1993-1995. Let d be the number of data packets handled monthly (in billions), and t be time in years since December, 1992. The best power model for this data is of the form where a = _____ and p= _____. Give both answers to 6 decimal places.

The formula for the power function whose values are in the following table is , where k = _____ and p = _____.

The horizontal asymptote of is y = _____. Enter "none" if there is no horizontal asymptote.

Suppose that a, b, and c are integers with a negative and odd, b positive and even, c positive and odd, and d positive and odd. Which of the following functions corresponds to the graph below?

The volume occupied by a fixed quantity of gas such as oxygen is inversely proportional to its pressure, provided that its temperature is held constant. Suppose that a quantity of oxygen occupies a 120 liter volume at a pressure of 16 atmospheres. If the temperature of the oxygen does not change, how many liters will it occupy if its pressure rises to 19 atmospheres? Round to 1 decimal place.

The following figure gives the graphs of four power functions. Which one could be the graph of ? If none of the graphs match, enter "none".

Which of the following statements are true for ? Mark all that apply.

It is possible for a rational function to have no zeros, such that for and for

Which of the following formulas has a graph with vertical asymptotes at x = 1 and x = 4, a horizontal asymptote at y = 1, and touches the x-axis at x = 2?

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

Let . The following figure shows the graph of , with a = _____.