Gasoline $ Problem

Question

The following graph shows the average retail price of regular gasoline in Tucson and Albuquerque over a 1-month period. Suppose T(d)represents the price of gas in Tucson as a function of the day, and A(d) represents the price of gas in Albuquerque as a function of the day. 

A) Consider the function (T−A)(d). What does it mean in practical terms if (T−A)(d) is…

A1) positive?

A2) negative?

A3) zero? 

B) Using the graphs below, determine the following:

B1) On what day(s) does (T−A)(d)=0?

B2) What is the lowest/most negative value of (T−A)(d)? On what date does that occur?

B3) What is the largest/most positive value of (T−A)(d)? On what date does that occur? 

Answer 1

(T - A)(d) = T(d) - A(d), where T(d) and A(d) are simply price values. Therefore, this notation represents the gas price difference of Tucson on a particular day and Albuquerque on the same day.

A1) If the result is positive, then the price in Tucson is greater than the amount being subtracted from Albuquerque.

(e.g., 3 - 2 = +1)

A2) If the result is negative, then the price being subtracted from Albuquerque is greater than the price in Tucson.

(e.g., 2 - 3 = -1)

A3) If the result is zero, then the prices from both cities is equal, and the difference is zero.

(e.g., 2 - 2 = 0)

B1) Look for the intersection points: between 2/7 and 2/8, as well as between 2/16 and 2/17

B2) Negative values can be identified when the red line (Albuquerque) is graphed above the blue line (Tucson). To find the lowest/most negative value, find the day where the distance between the red and blue lines is greatest, approximately 2/9.

B3) The positive difference values are identified when the blue line is above the red line, or Tucson price is greater than Albuquerque price. The largest/most positive value can be identified where the distance between the blue and red line is greatest, which is clearly seen on the last day, 2/26.