This is the first of two lessons where students learn to identify even functions and odd functions. A function is even if the outputs for and  are the same. Visually, the graph of appears symmetric across the vertical axis. Algebraically, we say that   for any input . A function is odd if the output for is the opposite of the output for . Visually, the graph of has a type of symmetry defined by successive reflections across both the - and -axes taking the graph of to itself. Algebraically, we say that  for any input .

In this lesson, students first identify key features of each type of function by sorting graphs into two groups. As their language is collected, displayed, and refined throughout the lesson, students increase the precision of their language in describing even and odd functions (MP6). As students compare tables of values and graphs in order to establish definitions for even and odd functions, they leverage the structure of even and odd functions (MP7).

Students will formalize these ideas in an upcoming lesson and learn to identify a function as even, odd, or neither from an equation, so there is no need for additional work with the definition given in the Lesson Synthesis.