Common Core State Standards for Mathematics
High School - Functions
Analyze functions using different representations
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
- Graph linear and quadratic functions and show intercepts, maxima, and minima.
- Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
- Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Build new functions from existing functions
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.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.
Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.
Grade Level Indicators (Grade 9)
Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.
Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.
Grade Level Indicators (Grade 10)
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
Principles and Standards for School Mathematics
Understand patterns, relations, and functions
analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;