Math 205 JW Lecture 4 - Compositions, Transformations, Linear models, Exponential models Intro

Welcome to lecture 4 of Math 205 JW - Elements of Calculus 1.

In tonight's lecture we continue our discussion of functions. We talk about composing functions and what it means as well as how to decompose functions (which would be useful later on when we get to things like the Chain Rule). We also talk about function transformations (reflecting, stretching, shrinking, shifting functions) and operations on functions (adding/subtracting, multiplying/dividing functions together).

We then move on to a special kind of function, the linear polynomial or linear functions, y = mx + b. We talk about the function, what its graph looks like and what its components mean. We do an example of a word problem that would use a linear function as a model to solve, and then talk about an important interpretation of slope--as a rate of change.

We then introduce another type of model, the exponential model. We talk about when this model is useful and we will discuss the kinds of functions used in this model in the next lecture.