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, in json format:
{
  "explanation": "This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.",
  "answer": "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: Analyze functions using different representations.

Model periodic phenomena with trigonometric functions.

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

Understand the concept of a function and use function notation.

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.

Prove and apply trigonometric identities.

Construct and compare linear and exponential models and solve problems.

Build new functions from existing functions.

Define, evaluate, and compare functions.

Interpret expressions for functions in terms of the situation they model.
problem_activity: Problem 1
Complete the table below to determine the process for finding the inverse of a function. The price of hats is written as a function of the number of hats,
$$h$$
, produced.
[IMG]
Problem 2
Below is a graph of a relation,
$$f$$
, represented as individual points.
[IMG]
Explain why the relation
$$f$$
is “not invertible.”


correct_option_index: 9