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

Prove and apply trigonometric identities.

Analyze functions using different representations.

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

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

Understand the concept of a function and use function notation.

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

Build new functions from existing functions.

Construct and compare linear and exponential models and solve problems.

Model periodic phenomena with trigonometric functions.

Define, evaluate, and compare functions.
problem_activity: Task
Below is a picture of the functions $f(x) = \log_b{x}$ and $g(x) = b^x$. In the application below, the base b varies between 1 and 2 (by hundredths) and pressing the "play" button will run through all possible values of b.
For which values of $b$ do the two graphs appear not to meet?
For which values of $b$ do the two graphs appear to meet in two points?
Check by evaluating the functions $f$ and $g$ that the two graphs meet at $x=e$ when $b = e^{\frac{1}{e}}$.


correct_option_index: 2

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