Use the structure of an expression to identify ways to rewrite it. For example, see x<sup>4</sup> – y<sup>4</sup> as (x<sup>2</sup>)<sup>2</sup> – (y<sup>2</sup>)<sup>2</sup>, thus recognizing it as a difference of squares that can be factored as (x<sup>2</sup> – y<sup>2</sup>)(x<sup>2</sup> + y<sup>2</sup>).
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.