Box B.1 - Sample NCTM Curriculum Standard Functions

In grades 9–12, the mathematics curriculum should include the continued study of functions so that all students can —

• model real-world phenomena with a variety of functions;
• represent and analyze relationships using tables, verbal rules, equations, and graphs;
• translate among tabular, symbolic, and graphical representations of functions;
• recognize that a variety of problem situations can be modeled by the same type of function;
• analyze the effects of parameter changes on the graphs of functions; and so that, in addition, college-intending students can —
• understand operations on, and the general properties and behavior of classes of functions...

The function concept also is important because it is a mathematical representation of many input-output situations found in the real world including those that recently have arisen as a result of technological advances. ...

Since functional relationships are encountered so frequently, the study of functions should begin with a sampling of those that exist in the students' world. Students should have the opportunity to appreciate the pervasiveness of functions through activities such as describing real-world relationships that can be depicted by graphs, reading and interpreting graphs, and sketching graphs of data in which the value of one variable depends on the value of another.

SOURCE: Excerpted from Commission on Standards for School Mathematics. 1989. Curriculum and Evaluation Standards for School Mathematics, National Council of Teachers of Mathematics, Reston, Va., pp. 154–155.