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

Analyze functions using different representations.

Define, evaluate, and compare functions.

Prove and apply trigonometric identities.

Understand the concept of a function and use function notation.

Model periodic phenomena with trigonometric functions.

Build new functions from existing functions.

Construct and compare linear and exponential models and solve problems.

Build a function that models a relationship between two quantities.

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

Use functions to model relationships between quantities.

Interpret expressions for functions in terms of the situation they model.
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: 1

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