**ERIC Number:**EJ1144423

**Record Type:**Journal

**Publication Date:**2017-Mar

**Pages:**7

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

Alphabet Soup

Rebholz, Joachim A.

Mathematics Teacher, v110 n7 p534-540 Mar 2017

Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse functions, and so on. Often, teachers ask students to graph a function given by its mathematical expression. This article focuses on the opposite process: Given the graph of a function, determine an explicit expression that results in the graph. The importance of such reasoning has been outlined in the Common Core Standards for Mathematics, where "Building Functions" has been identified as one of the main domains for the conceptual category "Functions" for high school students (CCSS 2010, p. 68). More specifically, in this domain, CCSS F-BF.1 states the specific skill "Determine an explicit expression, a recursive process, or steps for calculation from a context" (CCSS 2010, p. 70). The first two activities described were done early in the school year and led up to the main project. The author gave students in his grade 11 class the task of deciding which capital letters of the Roman alphabet can be represented as graphs of functions and then coming up with mathematical expressions for the corresponding functions. This project can be used as a capstone project, since it illustrates many concepts, such as the vertical line test, the definition of a function versus that of a relation, the domain and range of a function, inverse functions, symmetry, and transformations of functions.

Descriptors: Mathematics Instruction, High School Students, Secondary School Mathematics, Graphs, Mathematical Concepts, Mathematical Logic, Learning Activities, Grade 11, Alphabets, Teaching Methods

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: NCTM@nctm.org; Web site: http://www.nctm.org/publications/mathematics-teacher/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**High Schools; Secondary Education; Grade 11

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A