Name______Class Time ______

VARIABLE SENSE AND FUNCTION

4.1 and 4.2 MAT 104

In 2000, the U.S. Congress moved to reduce highway funding to states that did not implement a national standard of 0.08% blood-alcohol concentration as the minimum legal limit for drunk driving. By 2004, every state had adopted this limit. The following table represents a numerical description of the relationship between the number of beer consumed in 1 hour by a 200-pound person and his corresponding blood-alcohol concentration. In future problems, you may symbolically represent the number of beers consumed by the letter n, and the blood-alcohol concentration by B.

Number of Beers in an hour, n / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Blood-Alcohol Concentration(%)*, B / 0.018 / 0.036 / 0.054 / 0.072 / 0.090 / 0.108 / 0.126 / 0.144 / 0.162 / 0.180

*Based on the body weight of 200 pounds

  1. What is the input variable? What is the output variable?
  1. What is the blood-alcohol concentration for a 200-pound person who has consumed four beers in 1 hour? What about nine beers in 1 hour?
  1. According to the table, as the number of beers consumed in 1 hour increases, what happens to the blood-alcohol concentration?
  1. What is the maximum number of beers a 200-pound person can drink in 1 hour without exceeding the legal limit?
  1. Write an equation that relates the number of beers consumed to blood-alcohol concentration. (hint: what is the y – intercept?)
  1. Is this relation a function? Why or why not?
  1. Say you look at people who drank 4 beers in an hour. How would body weight effect the blood-alcohol concentration?

The semester is drawing to a close, and you are concerned about your grade in your math class. During the semester, you have already taken four exams and score 82, 75, 85, and 93. Your score on exam 5 will determine your final average for your math class.

  1. Identify the input and output variables.
  1. Four possible exam 5 scores are listed in the following table. Calculate the final average corresponding to each one, and record your answers.

EXAM 5 SCORE / FINAL AVERAGE
100
85
70
60
  1. Explain whether or not this relationship fits the definition of a function.
  1. Describe in words using sentences, how to obtain the final average for any given score on the fifth exam.
  1. Let A represent the final average and s represent the score on the fifth exam. Translate the verbal rule from problem 11 into a symbolic rule that expresses A in terms of s.
  1. What do you need to get on exam 5 to receive a final average of 89%

Often you want to emphasize the functional relationship between input and output. You do this symbolically by writing A(s), which reads, “A is a function of s.” The letter within the parentheses always represents the input variable, and the letter outside the parentheses is the function name and the output variable. For example A(100) = 87.

  1. Re-write your equation in problem 12 using this function notation.
  1. Evaluate A(95) and A(75).

DEFINITION

  1. Determine the practical domain of the final average function. Assume that no fractional parts of a point can be given and that the exam has a total of 100 points.
  1. What is the domain of the function, where W and s have no contextual significance?
  1. Show or explain how you would fine the practical range for the average value function and interpret the meaning of this range.
  1. You are on your way to take your fifth math exam. The gas gauge on your car indicates that you are almost out of gas. Gas costs $3.76 per gallon and you need to figure out if you can fill up your 14 gallon gas tank with the money you have with you.
  2. Identify a reasonable input and output variable in this situation.
  1. Write a verbal rule (using words) to determine the cost for any given number of gallons pumped.
  1. Let C represent the cost of the gas purchased and g represent the number of gallons pumped. Translate the verbal rule into a symbolic rule for C in terms of g using function notation.
  1. What is the practical domain of this function?
  1. What is the practical range for this function?
  1. Determine C(12). Interpret the answer in the context of the problem.