This Warm-up prompts students to compare four unlabeled graphs. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Students need to look for and make use of the structure of the graphs to determine how each one is like or unlike the others (MP7).

Invite each group to share one reason why a particular set of three goes together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.

During the discussion, ask students to explain the meaning of any terminology they use, such as “intercepts,” “minimum,” or “linear functions.” Also, press students on unsubstantiated claims.

In this activity, students are given the same four graphs they saw in the Warm-up and four descriptions of functions and are asked to match them. All of the functions share the same context. Students then use these features to reason about a likely domain and range of each function.

To make the matches, students analyze and interpret features of the graphs, looking for and making use of structure in the situation and in the graphs (MP7). Here are some possible ways students may reason about each match:

• The swing goes up and down while the child is swinging, so D could be a graph for function .
• The time left on the swing decreases as the time on the swing increases, so A is a possible graph for function .
• The distance of the child from the top beam of the swing doesn't change as long as the child is on the swing, so C is a possible graph for function .
• The total number of times the swing is pushed must be a counting number and cannot be fractional. Graph B has multiple pieces, and each one could represent the total number of push for certain intervals of time, so B is a possible graph of .

Students reason quantitatively and abstractly as they connect verbal and graphical representations of functions and as they think about the domain and range of each function (MP2).

In this activity, students continue to interpret a graph of a function in terms of a situation and relate the features of the graph to the domain and range of the function. The context is a familiar one, allowing students to focus their reasoning on domain and range.

Unlike in the activity about a child on a swing, the graph includes a scale on each axis and the coordinate pairs of some points, allowing students to identify the range more definitively. On the other hand, the graph is a partial representation of the function, as it does not show what happens after a dropped ball hits the ground the fifth time. When describing the domain, students need to attend to what is reasonable in this situation (that is, noting that the ball likely does not just stop after the fifth bounce).