Instruction
Directions:
Find, in a publication, a graph of a function that represents a real world situation, or make up your own graph of a function that could represent a real world situation. The graph you use for this assignment must exhibit at least six aspects that we discussed in class. You are to make a chart indicating each aspect of the graph, where it occurs, and what it indicates about the function or its derivatives. Then you are to write a narrative in which you explain the connection between each graph aspect and the real world situation it represents. The final paper that you submit must include the graph, the chart, and the narrative.
Graph concepts include, but are not limited to:
domain
x- and y-intercepts
horizontal and vertical asymptotes
limit
left/right limit
continuity
left/right continuity
types of discontinuity: removable, jump, infinite
slope of tangent
increasing/decreasing
maximum/minimum
concavity
inflection point
Example Topics:
Some examples of situations for which students have created their own graph are:
a graph of Joe Function’s trip through the land of Graphia where a removable discontinuity is represented by a trap
a graph of AnakinSkywalker/DarthVadar’s relationship with the force where the x-intercepts represent his changes from the “good side” to the “dark side” and back again
a graph of profits for Computer Totes, Inc., where a fire in the factory created a jump discontinuity. The narrative written by the student in this paper was in the form of a newspaper articles
a graph depicting a student’s road trip across the states
a graph of energy level of a chemical reaction with respect to time
a graph of a student’s interest in watching their favorite movie through the years
a graph of the population of Greyhound Lake with a description of Carrying Capacity and Overshots
a graph of students’ stress levels as deadlines approach
Some examples of graphs students found in publications are:
a graph of power levels in thermal megawatts of the Chernobyl nuclear power plant accident where there is a vertical asymptote at 1:23 a.m. on April 16, 1986
a graph of tourism in Israel during 1989 to 1994 with an absolute minimum occurring during the Persian Gulf War
a graph of the unemployment percentage where it is increasing at an increasing rate between 1989 and 1992
a graph of the number of regular seasonal wins by Pittsburgh Steelers within the Roethlisberger era
a graph of the percentage of players vs. player global sync in the game Assasin’s Creed