options: Define, evaluate, and compare functions.

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.

Prove and apply trigonometric identities.

Understand the concept of a function and use function notation.

Construct and compare linear and exponential models and solve problems.

Use functions to model relationships between quantities.

Analyze functions using different representations.

Extend the domain of trigonometric functions using the unit circle.

Model periodic phenomena with trigonometric functions.
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: 9