few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response, in json format:
{
  "explanation": "An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation. Solving this problem does not require use of the Pythagorean identity.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS
options: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.  For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
problem_activity: Categorize each representation of a function as linear, exponential, or quadratic. Explain your reasoning for each one.
|                                                                                                                               a.                                                                                                                               |                                                                                                                             $$x$$                                                                                                                              | $$y$$ | 1 | -2 | 2 | 1 | 3 | 6 | 4 | 13 | 5 | 22 | b. | $$x$$ | $$y$$ | 1 | 48 | 2 | 24 | 3 | 12 | 4 | 6 | 5 | 3 |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------|---|----|---|---|---|---|---|----|---|----|----|-------|-------|---|----|---|----|---|----|---|---|---|---|
|                                                                                                                             $$x$$                                                                                                                              |                                                                                                                             $$y$$                                                                                                                              |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               1                                                                                                                                |                                                                                                                               -2                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               2                                                                                                                                |                                                                                                                               1                                                                                                                                |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               3                                                                                                                                |                                                                                                                               6                                                                                                                                |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               4                                                                                                                                |                                                                                                                               13                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               5                                                                                                                                |                                                                                                                               22                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                             $$x$$                                                                                                                              |                                                                                                                             $$y$$                                                                                                                              |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               1                                                                                                                                |                                                                                                                               48                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               2                                                                                                                                |                                                                                                                               24                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               3                                                                                                                                |                                                                                                                               12                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               4                                                                                                                                |                                                                                                                               6                                                                                                                                |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               5                                                                                                                                |                                                                                                                               3                                                                                                                                |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                            c.                       $$f(x)=x(x-4)$$                                                                                                            |                                                                                                         d.                       $$f(x)=4-{x\over2}$$                                                                                                          |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
| e.            |https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_tte.PNG|  |https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_tte.PNG| image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_tte.PNG | f.            |https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_ttf.PNG|  |https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_ttf.PNG| image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_ttf.PNG |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |


correct_option_index: 1