In this lesson, students use the term maximum (or minimum) to talk about the value of a function that is greater than or equal to (or less than or equal to) all the other values. They also use the terms horizontal intercept and vertical intercept to describe the points where a graph crosses the horizontal and vertical axes. Students also interpret graphs more holistically using the terms increasing and decreasing to describe where a function’s values get greater or lesser as the graph is read left to right.

Students relate these features of graphs to features of the functions represented. For instance, they look at an interval in which a graph shows a positive slope and interpret that to mean an interval in which the function’s values are increasing. Students also use statements in function notation, such as and , to talk about key features of a graph.

By now, students are familiar with the idea of intercepts. Note that in these materials, the terms “horizontal intercept” and “vertical intercept” are used to refer to intercepts more generally, especially when a function is defined using variables other than and . If needed, clarify these terms for students who may be accustomed to using only the terms “-intercept” and “-intercept.”

As students look for connections across representations of functions and relate them to quantities in situations, they practice making sense of problems (MP1) and reasoning quantitatively and abstractly (MP2). Using mathematical terms and notation to describe features of graphs and features of functions calls for attention to precision (MP6).