Ohio Resource Center
Content Supports - Reference materials
Pre-Calculus
Discipline
Mathematics
12, Postsecondary
Professional Commentary

Students will find tutorials, Java applets, drills, computer programs, quizzes, and LiveMath notebooks and animations on a variety of precalculus topics. More than 100 subsections of the site address polynomial, rational, exponential, trigonometric, and logarithmic functions, as well as piecewise definitions, parametric equations, and polar coordinates. Other specific topics include conic sections, even and odd functions, solving equations, and curve fitting. Graphing calculators are used throughout the activities. This site is one of several Visual Calculus sites developed by the mathematics department at the University of Tennessee. (sw)

Common Core State Standards for Mathematics
High School - Functions
Interpreting Functions
Analyze functions using different representations
Building Functions
Build new functions from existing functions
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
B.
Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.
E.
Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.
F.
Solve and graph linear equations and inequalities.
G.
Solve quadratic equations with real roots by graphing, formula and factoring.
H.
Solve systems of linear equations involving two variables graphically and symbolically.
Benchmarks (11–12)
A.
Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
9.
Solve linear equations and inequalities graphically, symbolically and using technology.
10.
Solve 2 by 2 systems of linear equations graphically and by simple substitution.
11.
Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution.
12.
Solve simple quadratic equations graphically; e.g., y = x² - 16.
1.
Define function with ordered pairs in which each domain element is assigned exactly one range element.
4.
Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words.
5.
Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum.
6.
Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form.
9.
Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.
10.
Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology.
1.
Define function formally and with f(x) notation.
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.
7.
Solve systems of linear inequalities.
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.
4.
Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology.
6.
Represent the inverse of a function symbolically and graphically as a reflection about y = x.
10.
Describe the characteristics of the graphs of conic sections.
11.
Describe how a change in the value of a constant in an exponential, logarithmic or radical equation affects the graph of the equation.
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.
4.
Represent the inverse of a transcendental function symbolically.
9.
Translate freely between polar and Cartesian coordinate systems.
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;
understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions;
Represent and analyze mathematical situations and structures using algebraic symbols
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;
understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions;
write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases;
use a variety of symbolic representations, including recursive and parametric equations, for functions and relations;
judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.