Common Core State Standards for Mathematics
High School - Functions
Building Functions
Build new functions from existing functions
HSF-BF.B.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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Trigonometric Functions
Model periodic phenomena with trigonometric functions
HSF-TF.B.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
E.
Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.
Benchmarks (11–12)
A.
Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
Grade Level Indicators (Grade 10)
2.
Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range.
Grade Level Indicators (Grade 11)
4.
Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology.
Grade Level Indicators (Grade 12)
3.
Describe and compare the characteristics of transcendental and periodic functions; e.g., general shape, number of roots, domain and range, asymptotic behavior, extrema, local and global behavior.
Principles and Standards for School Mathematics
Algebra Standard
Understand patterns, relations, and functions
Expectations (9–12)
analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;
understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions;