options: Model periodic phenomena with trigonometric functions.

Analyze functions using different representations.

Construct and compare linear and exponential models and solve problems.

Use functions to model relationships between quantities.

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

Prove and apply trigonometric identities.

Build a function that models a relationship between two quantities.

Define, evaluate, and compare functions.

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

Understand the concept of a function and use function notation.

Build new functions from existing functions.

Extend the domain of trigonometric functions using the unit circle.
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

2

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