Lesson 4

Reflecting Functions

Lesson Narrative

In this lesson, students compare two functions, where one is a reflection of the other across an axis, using tables, graphs and equations, making connections to their previous study of reflections in geometry. They continue to work with function notation where one function is defined in terms of another.

Students begin by observing three graphs which show reflections across both the \(x\)- and \(y\)-axis. The warm-up gives them opportunities to see and make use of structure (MP7) by noticing that the distance of each point on the graph to the line of reflection is the same, but in a different direction. Students then study reflections across each of the axes individually, identifying what does and does not change for specific points on the graph being reflected. The work in this lesson builds directly into the two following lessons where students study even and odd functions, so there is no need to introduce these terms at this time.

Learning Goals

Teacher Facing

  • Comprehend that "reflecting" a function's graph across an axis means replacing either the inputs or the outputs with their opposite values.
  • Create a graph of $y=\text-f(x)$ or $y=f(\text-x)$ given the graph of $y=f(x)$.

Student Facing

  • Let’s reflect some graphs.

Required Materials

Required Preparation

Provide access to colored pencils, two colors per student.

Provide access to tracing paper for students who need support visualizing the reflections throughout the lesson.

Learning Targets

Student Facing

  • I can reflect a graph across either the $x$- or $y$-axis.

CCSS Standards

Addressing

Building Towards