This lesson integrates technology to allow students to explore families of functions. Students must know translations of quadratic functions in order to complete this activity. Further knowledge of functions is valuable but not necessary.
This lesson also requires the use of Geogebra--a free interactive geometry software. A web version is available, but the instructions are specific for the Windows downloaded version. This lesson could easily be adapted to any Geogebra version.
3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.