Assignment 3: Due before start of class 14 Sep 2023:

The goal of this assignment is to increase your skill and familiarity in relating various basic functions to their graphical representation, and vice versa. Before class, please send me a PDF of your explorations, and come to class prepared to discuss and share your observations.

For each parameter in each function, you should be able to describe how you would measure or interpret that parameter from its graph.

1. Using Shodor's MultiFunctionDataFlyer as an exploratory tool, in your notes, (I recommend one page per function) parameterize and sketch the shape and variations for each of the following:
   • Constant Function y(x) = a
   • Linear Function y(x)= m*x + b
   • Quadratic Function in general form: y(x) = a*x^2 + b*x + c
   • Quadratic Function in vertex (or standard) form: y(x) = a*(x-h)^2 + k
   • Trigonometric Functions of the form: y(x) = a*cos(b*(x-c)) + d
   • Exponential Function (try both positive and negative exponents) y(x) = a*exp(b*(x-c)) + d
   • Logistic Function: There are many you could try, for example, y(x) = a*exp(-(b/x)^n)+c
     NOTE: click option to let exponents change for the Logistic example above
   • Gaussian Function: For example, y(x) = a*exp(-b*(x-c)^2)+d

2. Think about examples of some phenomena in your major field of study or personal interest that has the observed shape/behavior.