In this section, students recall the definition of a function as a rule that assigns no more than one output to every input. Then, they use function notation, like or , to describe rules from real-world situations and understand how the notation differentiates between input and output values.

In this section, students focus on the domain and range of various functions. The language of domain and range allows students to better understand piecewise functions for which different rules apply to different parts of the domain.

A graph, with origin O. The horizontal axis, age, years, scale from 0 to 16 by 1s. The vertical axis, train fare, dollars, scale from 9 to 8 by 1s. A horizontal line segment, with open circle endpoints, begins at 0 comma 0 and ends at 5 comma 0. A horizontal line segment begins with a closed circle at 5 comma 5 and ends with an open circle at 11 comma 5. A line segment begins with a closed circle at 11 comma 7 and ends with an open circle at 16 comma 7.

This section has two lessons that may be optional, depending on your state requirements. The lessons address solving absolute value equations and inequalities.

In this section, students focus on a particular piecewise function, . They rely on their understanding from earlier grades of absolute value as a distance to graph a situation, then interpret it as a piecewise function. Later, they solve equations and inequalities that involve absolute values by reasoning about distance as well as interpreting them as cases from the piecewise definition.

In this section, students analyze graphs of functions including special features, such as “maximum,” “minimum,” “intercepts,” and “average rate of change.” They make connections between descriptions of real-life situations and graphs of functions that model those situations. Then they compare situations using graphs and function notation.

In this final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions.

In this section, students work with inverse functions as a way to find input values that correspond to known output values. Initially, students use the idea of writing a secret code to motivate the need to find the input that produced a given output. Then, they are provided contexts in which it is efficient to use the inverse to find inputs when several different outputs are known, such as converting between currencies or temperature scales.