few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Prove and apply trigonometric identities.

Use functions to model relationships between quantities.

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

Define, evaluate, and compare functions.

Build a function that models a relationship between two quantities.

Construct and compare linear and exponential models and solve problems.

Model periodic phenomena with trigonometric functions.

Extend the domain of trigonometric functions using the unit circle.

Understand the concept of a function and use function notation.

Build new functions from existing functions.

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

Analyze functions using different representations.
problem_activity: Given:
$${{f(x)}=\mathrm{cos}(2x)}$$
$${g(x)=-\mathrm{cos}(x)}$$
[IMG]
a.   Describe the period, amplitude, and midline of the function
$${f(x)}$$
.
b.   Where is
$${f(x)}=g(x)$$
over the domain of
$${0\leq x \leq 2\pi}$$
?


correct_option_index: 0