Students investigate the effect of the sign of the leading coefficient on the end behavior of the function. They begin by matching a graph with “flipped” end behavior to an equation by focusing on the structure of the equation (MP7). Then they write equations of polynomials that meet a list of criteria, such as having an odd degree and specific end behavior. The last activity asks students to consider two functions with matching end behavior for positive input values and decide which is greater, which reinforces the idea that the end behavior of a function can be determined completely by focusing on the leading term. 

When explaining their thinking to the class, students will need to use precise language and be clear about what they mean by “greater” (MP6).

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making graphing technology available.

The goal of today’s exercise is to use the suggestions from the previous exercise to revise the “Norms” sections of the Math Community Chart and to invite students to reflect on one norm that will be a strength for them. Both activities begin to build shared accountability for and investment in the classroom norms.