options: Model periodic phenomena with trigonometric functions.

Understand the concept of a function and use function notation.

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

Build new functions from existing functions.

Build a function that models a relationship between two quantities.

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

Define, evaluate, and compare functions.

Extend the domain of trigonometric functions using the unit circle.

Use functions to model relationships between quantities.

Construct and compare linear and exponential models and solve problems.

Prove and apply trigonometric identities.

Analyze functions using different representations.
problem_activity: Task
Imagine Scott stood at zero on a life-sized number line.  His friend flipped a coin 50 times.  When the coin came up heads, he moved one unit to the right. When the coin came up tails, he moved one unit to the left. After each flip of the coin, Scott's friend recorded his position on the number line. Let $f$ assign to the whole number $n$, when $1 \leq n \leq 50$,
Scott's position on the number line after the $n^{\rm th}$ coin flip.
If $f(6) = 6$ what can you conclude about the outcomes of the first $6$ coin
tosses?  Explain.  What if $f(6) = -4$?
Is it possible that $f(7) = 2$?  Explain.
Find all integers $m$ so that the probability that $f(50) = m$ is zero.


correct_option_index: 1