Compare quadratic functions with linear and exponential functions
• Distinguish between tables representing linear, exponential, and quadratic functions (F-LE.A.3$^\star$).
• Distinguish between graphs of linear, exponential, and quadratic functions (F-LE.A.3$^\star$).
• Use precise language to describe properties that distinguish linear, exponential, and quadratic functions (F-LE.A.3$^\star$).
Now that students have been introduced to quadratic functions they compare them with the two other families of functions they have studied, linear and exponential functions. They compare tables and graphs and describe the differences. They also compare the growth of increasing quadratic functions with the growth of increasing linear functions or increasing exponential functions.
WHAT: In Identifying Functions students compare tables and attempt to determine what types of functions the tables could represent. They look for constant differences, constant ratios, or, in the case of quadratics, constant second differences.
WHY: The purpose of this task is for students to use precise language in describing the various types of functions they have seen before and the new one they are exploring. A desirable outcome of a lesson based on this task would be concrete definitions with tables, graphs and written descriptions of each type of function (MP2, MP6).
WHAT: In this task students are given the graphs of a quadratic and an exponential function and are asked to choose which is which and come up with equations for them.
WHY: This Daily Desmos requires students to think more carefully about the properties of exponential and quadratic functions than simply observing their shape, since the two graphs are quite similar (F-LE.A.3$^\star$). The use of Desmos as a tool to understand graphs will also help them as they continue their study of quadratic functions (MP5).