Activity 2a – Transformations of Functions and their Graphs

This activity prepares students for graphing sine and cosine waves. It should help students understand Topic 2.2 (Amplitude), Topic 2.3 (Frequency, Wavelength and Period) and Topic 2.5 (Phase Shift). It does not depend on any knowledge of the graphs of [latex]y = \sin \; x[/latex], or [latex]y = \cos \; x,[/latex] and therefore is a good way to introduce the unit on graphing trig functions. The activity does rely on functions from algebra, and may also serve as a review of these functions.

A student preparing for Calculus should at some point be familiar with the graphs of a Catalog of Common Functions, such as lines ([latex]y = mx + b[/latex]), parabolas ([latex]y = x^2[/latex]) and other power functions ([latex]y = x^3, x^4, x^5 \ldots[/latex]), the reciprocal function ([latex]y = 1/x[/latex]), exponential functions [latex](y = Ke^{rt}[/latex], [latex]y = Ke^{-rt}[/latex]) and logarithmic functions ([latex]y = \ln \; x[/latex], [latex]y = \log \; x[/latex]), as well as the trig functions. The focus here is that once you have learned a basic graph, like [latex]y = \sin \; x[/latex], you will then be able to shift, stretch and flip that graph to find new graphs.

General Graphing