Ohio Resource Center
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Content Supports
Functions and Transformations of Functions
Discipline
Mathematics
Grades
11, 12, Postsecondary
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Professional Commentary

This tutorial begins with the definition of function and illustrates the graph, domain, and range of several nonlinear functions. These same functions are used to illustrate even (symmetric about the y-axis) and odd (symmetric about the origin) functions. The effect of a horizontal translation, a vertical translation, a change of amplitude, and a change of scale on the graph of a function is illustrated. An applet is provided for students to explore the results of these transformations on three different functions. (sw)


Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (11–12)
A.
Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
Grade Level Indicators (Grade 11)
3.
Describe and compare the characteristics of the following families of functions: quadratics with complex roots, polynomials of any degree, logarithms, and rational functions; e.g., general shape, number of roots, domain and range, asymptotic behavior.
5.
Identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis or y = x.
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 perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions;