The purpose of this activity is to demonstrate a process for solving an equation written in function notation.

This activity uses the Worked Example routine. In this routine, students analyze steps used to solve a problem and discuss specific steps with a partner and the whole class. During the discussions, students construct viable arguments to justify the steps taken by the problem solver (MP3). Later, students can apply these strategies to solve similar problems.

The purpose of this discussion is to develop student understanding of solving equations written in function notation.

Tell students to open their books or devices. Display the following questions, and give students 1–2 minutes of quiet think time to consider their responses.

• “Why does 9.2 appear twice in the first step?” (Since we are finding the value of in the equation , each in the equation is replaced with 9.2. There were two ’s in the equation, so there are two 9.2’s in the first step.)
• “Why does stay rather than being multiplied together?” (While looks like multiplication, is the name of the function. means “the value of function when the input is 9.2.” It does not mean “ multiplied by 9.2.”)
• “What does the answer mean?” (When the input of function is 9.2, the output is 22.6.)

Ask partners to compare their responses to each question and to decide if either or both answers are correct. During this partner discussion, monitor to select groups who reason about the questions in different ways. Follow with a whole-class discussion, inviting 1–2 selected groups to share their answers for each question.

If time allows, consider displaying a second worked example next to the first that either:

• Shows a different method of solving a similar problem that students can compare and contrast with the first example (MP7). For example, giving the output and asking students to find the input.
• Shows the same method with an error that students can critique and correct (MP3). For example, showing a mistake in the order of operations.

In this activity, students connect a function to its meaning in a situation. Students interpret the input and output as well as use the function to find the output for a given input and the input for a given output. In the associated Algebra 1 lesson, students interpret different representations in the context of the problem. This activity supports students by allowing them to focus on one representation, the equation. As students interpret their answers in the context of this situation, they reason abstractly and quantitatively (MP2).

In this activity, students interpret two functions in the same situation. They compare outputs for the same input and inputs for the same outputs. In the associated Algebra 1 lesson, students interpret functions in context using multiple representations of the functions. Students are supported in this activity by being asked to consider only the equation and graphical representations. Students make sense of problems and persevere in solving them when comparing values and deciding which company should be used (MP1).