options: Build new functions from existing functions.

Define, evaluate, and compare functions.

Use functions to model relationships between quantities.

Prove and apply trigonometric identities.

Extend the domain of trigonometric functions using the unit circle.

Construct and compare linear and exponential models and solve problems.

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

Build a function that models a relationship between two quantities.

Analyze functions using different representations.

Model periodic phenomena with trigonometric functions.

Understand the concept of a function and use function notation.

Interpret expressions for functions in terms of the situation they model.
problem_activity: Task
A wheel of radius 0.2 meters begins to move along a flat surface so that the center of the wheel moves forward at a constant speed of 2.4 meters per second.  At the moment the wheel begins to turn, a marked point $P$ on the wheel is touching the flat surface.
[IMG]
Write an algebraic expression for the function $y$ that gives the height (in meters) of the point $P$, measured from the flat surface, as a function of $t$, the number of seconds after the wheel begins moving.
Sketch a graph of the function $y$ for $t>0$.  What do you notice about the graph?  Explain your observations in terms of the real-world context given in this problem.
We define the horizontal position of the point $P$ to be the number of meters the point has traveled forward from its starting position, disregarding any vertical movement the point has made.  Write an algebraic expression for the function $x$ that gives the horizontal position (in meters) of the point $P$ as a function of $t$, the number of seconds after the wheel begins moving.
Sketch a graph of the function $x$ for $t>0.$  Is there a time when the point $P$ is moving backwards?  Use your graph to justify your answer.


correct_option_index: 6

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