This lesson continues the work begun in the previous lesson of understanding the relationship between an equation of a polynomial function and the end behavior of the function.
Now that students have seen the differences in end behavior between polynomials of even and odd degree, they examine the effect of the sign of the leading coefficient on end behavior. First students match 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 leads back to 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 be clear about what they mean by “greater” (MP3). Throughout the lesson, students are asked to describe the end behavior of polynomials with precision (MP6).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems (MP5). We recommend making technology available.
- Comprehend how the sign of the leading coefficient of a polynomial function affects the end behavior.
- Create equations for polynomial functions with specific end behavior.
- Let’s describe the end behavior of polynomials.
- Small slips of paper, 1 per student
- I can identify the end behavior of a polynomial function from its equation.
How the outputs of a function change as we look at input values further and further from 0.
This function shows different end behavior in the positive and negative directions. In the positive direction the values get larger and larger. In the negative direction the values get closer and closer to -3.