options: Construct and compare linear and exponential models and solve problems.

Build new functions from existing functions.

Prove and apply trigonometric identities.

Define, evaluate, and compare functions.

Model periodic phenomena with trigonometric functions.

Build a function that models a relationship between two quantities.

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

Extend the domain of trigonometric functions using the unit circle.

Use functions to model relationships between quantities.

Analyze functions using different representations.

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

Understand the concept of a function and use function notation.
problem_activity: Task
How do the values of the three functions $f(x) = 2x$, $g(x) = x^2$ and $h(x) = 2^x$ compare for large positive and negative values of $x$?
Explain
your findings from part (a) for $f$ and $g$ by studying the quotients $\frac{g(x)}{f(x)}$.
Explain your findings from part (a) for $g$ and $h$ by studying $\frac{g(x+1)}{g(x)}$ and $\frac{h(x+1)}{h(x)}$ for different values of $x$.


correct_option_index: 0