options: Build a function that models a relationship between two quantities.

Understand the concept of a function and use function notation.

Extend the domain of trigonometric functions using the unit circle.

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

Construct and compare linear and exponential models and solve problems.

Prove and apply trigonometric identities.

Analyze functions using different representations.

Build new functions from existing functions.

Use functions to model relationships between quantities.

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

Model periodic phenomena with trigonometric functions.

Define, evaluate, and compare functions.
problem_activity: Warm-up
In this warm-up, students revisit quadratic expressions in different forms and what the expressions reveal about the graphs that represent them. They match equations and graphs representing two quadratic functions. The axes of the graphs are unlabeled, so students need to reason abstractly about the parameters in the expressions and the features of the graphs.
Student Facing
[IMG]
Here are graphs representing the functions
\(f\)
and
\(g\)
, given by
\(f(x) = x(x+6)\)
and
\(g(x) = x(x+6)+4\)
.
Which graph represents each function? Explain how you know.
Where does the graph of
\(f\)
meet the
\(x\)
-axis? Explain how you know.
Student Response
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Activity Synthesis
Invite students to share their matches and explanations. If one or more explanations in the Student Response are not mentioned, bring them up so that students can see multiple ways of reasoning about the equations and graphs.


correct_option_index: 6