options: Extend the domain of trigonometric functions using the unit circle.

Use functions to model relationships between quantities.

Model periodic phenomena with trigonometric functions.

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

Construct and compare linear and exponential models and solve problems.

Understand the concept of a function and use function notation.

Build new functions from existing functions.

Define, evaluate, and compare functions.

Prove and apply trigonometric identities.

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.
problem_activity: Task
Sketch the graphs of the functions described by $\displaystyle f(x)=x^2$ and $\displaystyle g(x)=x^4$ on the same axes, being careful to label any points of intersection.  Also, find and label $\displaystyle\left(\frac{1}{2}, f(\frac{1}{2})\right)$ and $\displaystyle\left(\frac{1}{2}, g(\frac{1}{2})\right)$.
Sketch the graphs of the functions described by $f(x)=x^3$ and $g(x)=x^5$ on the same axes, being careful to label any points of intersection. Also, find and label $\displaystyle\left(\frac{1}{2}, f(\frac{1}{2})\right)$ and $\displaystyle\left(\frac{1}{2}, g(\frac{1}{2})\right)$.
Sketch the graphs of the functions described by $f(x)=x^2$ and $g(x)=x^3$ on the same axes, being careful to label any points of intersection. Also, find and label $\displaystyle\left(\frac{1}{2}, f(\frac{1}{2})\right)$ and $\displaystyle\left(\frac{1}{2}, g(\frac{1}{2})\right)$.


correct_option_index: 11