Students explore and manipulate expressions based on the following statement:

A function f defined for -a < x < a is even if f(-x)=f(x) and is odd if f(-x)=-f(x) when -a < x < a. In this task we assume f is defined on such an interval, which might be the full real line (i.e., a=8).

### General Information

**Subject(s):**Mathematics

**Grade Level(s):**9, 10, 11, 12

**Freely Available:**Yes

**Keywords:**sum of even and odd, sum, even, odd, function, greater than, less than, negative, infinity, equations, system, denominator, numerator, cpalms, icpalms, illustrativemathematics.org, illustrative mathematics, tasks, mathematics, math, Florida standards, resource, free, freely available, problems-based learning, student activities

**Instructional Component Type(s):**

**Problem-Solving Task**

**Resource Collection:**Illustrative Mathematics