Standard: F-IF.4

Subject Area: Mathematics (NYS P-12 Common Core)

Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade

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.★

Standard: F-BF.3

Subject Area: Mathematics (NYS P-12 Common Core)

Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade

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.

Standard: F-LE.3

Subject Area: Mathematics (NYS P-12 Common Core)

Grades: Commencement, 9th Grade, 10th Grade, 11th Grade, 12th Grade

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.