The course begins by revisiting foundational ideas you will need in this course (quantity, variable, function, rate of change) from the perspective of what they mean and how they are used when modeling dynamic phenomena with functions. It is through solidifying your understanding of these ideas that you will be equipped to use your mathematical thinking to model dynamic quantitative relationships in this and subsequent courses in mathematics and science.

As you approach this course, it will be useful to keep in mind that a cross-cutting focus is on understanding and using functions to represent how two quantities’ values vary together. You will engage with online lessons, in-class investigations, and online homework scaffolded to support you in becoming fluent and confident in representing quantitative growth patterns using functions (e.g., linear, exponential, rational, trigonometric)—as such, it will be useful for you to view a function formula and graph as a way of specifying (or constraining) how two quantities’ values are related and vary together (e.g., amount of money earned and number of hours worked; number of bacteria in a culture and number of minutes since taking the sample). This is the thinking that allows you to create the specific formula or graph that relates the two quantities’ values.

As we visit each function type, we will also apply algebraic methods such as simplifying, factoring, or completing the square to determine a representationally equivalent algebraic statement with a different form. In addition, we will review the purpose of changing the form of an algebraic expression (such as factoring to determine roots/zeros) and practice these methods to assure fluency. We will explore uses of solving equations and evaluating functions as a means of finding specific values of one quantity (amount of money earned) when a specific value of the other quantity (number of hours worked) is known.