options: Build new functions from existing functions.

Interpret functions that arise in applications in terms of the context.

Interpret expressions for functions in terms of the situation they model.

Understand the concept of a function and use function notation.

Analyze functions using different representations.

Use functions to model relationships between quantities.

Extend the domain of trigonometric functions using the unit circle.

Build a function that models a relationship between two quantities.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.

Model periodic phenomena with trigonometric functions.

Prove and apply trigonometric identities.
problem_activity: Warm-up
The purpose of this warm-up is for students to notice and describe the features of graphs using their own language. Students will encounter a variety of graphs over the next several lessons and throughout these lessons they will gradually develop more precise language around graphs as the needs of activities dictate.
Launch
Arrange students in groups of 2–4. Display the image of the four graphs for all to see. Ask students to indicate when they have noticed one figure that does not belong and can explain why. Give students 1 minute of quiet think time and then time to share their thinking with their group. Follow with a whole-class discussion.
Student Facing
Which graph doesn’t belong?
[IMG]
Student Response
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Activity Synthesis
After students have conferred in groups, invite each group to share one reason why a particular graph might not belong. Record and display the responses for all to see. After each response, ask the rest of the class if they agree or disagree. Since there is no single correct answer to the question of which graph does not belong, attend to students’ explanations and ensure the reasons given are correct.
Try to highlight the two facts that there are points with the same first coordinate and different second coordinates in graph B (which means it is not a function), the straight segments of C vs. curves of the others, and the discrete nature of D during this discussion, using whatever language students bring to it. Avoid introducing the traditional
\(x\)
and
\(y\)
names for the axes into the discussion unless students use them first. More formal vocabulary will be developed in later activities, lessons, and grades, and much of the motivation of this added vocabulary is to improve upon the somewhat clunky language we are led to use without it.


correct_option_index: 9