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

Extend the domain of trigonometric functions using the unit circle.

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

Use functions to model relationships between quantities.

Prove and apply trigonometric identities.

Build a function that models a relationship between two quantities.

Build new functions from existing functions.

Model periodic phenomena with trigonometric functions.

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

Define, evaluate, and compare functions.

Analyze functions using different representations.

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