Math 205 Lecture 4 - Function compositions, Transformations and Straight lines

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

In today's lecture we continue our discussion of functions. We look at how to tell if functions are increasing or decreasing (this will be very important later) and we also look at how to compose functions (plug functions into other functions) and examine the domains of those. We quickly refresh our memory of transformations of functions (horizontal and vertical shifts, stretches, shrinking and reflecting) and talk about the symmetry of even and odd functions.

We end by beginning a "new" topic, linear models, where we talk about (one form of) the equation of a line, and its slope. We shall continue this discussion in the next lecture, and then move on to exponential and logarithmic functions.