options: Build new functions from existing functions.

Define, evaluate, and compare functions.

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

Use functions to model relationships between quantities.

Construct and compare linear and exponential models and solve problems.

Model periodic phenomena with trigonometric functions.

Analyze functions using different representations.

Extend the domain of trigonometric functions using the unit circle.

Build a function that models a relationship between two quantities.

Prove and apply trigonometric identities.

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

Understand the concept of a function and use function notation.
problem_activity: Task
The table below shows some input-output pairs of two functions $f$ and $g$ that agree for the values that are given but some of their output values are missing.
|  $t$   |   |   |   |   |   |   |   |   |
|--------|---|---|---|---|---|---|---|---|
| $f(t)$ |   |   |   |   |   |   |   |   |
| $g(t)$ |   |   |   |   |   |   |   |   |
Complete the table in a way so that $f$ could be invertible and so that $g$ is definitely not invertible.
Graph both functions and explain from the graph why $f$ is invertible and $g$ is not.
Come up with two real life situations that $f$ and $g$ could be representing.
Find and interpret the value $f^{-1}(4)$ in terms of these contexts.


correct_option_index: 0