options: Model periodic phenomena with trigonometric functions.

Build new functions from existing functions.

Build a function that models a relationship between two quantities.

Analyze functions using different representations.

Understand the concept of a function and use function notation.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.

Extend the domain of trigonometric functions using the unit circle.

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

Use functions to model relationships between quantities.

Prove and apply trigonometric identities.

Interpret expressions for functions in terms of the situation they model.
problem_activity: Problem 1
Consider the sequence below.
$${1, \space1,\space 2,\space 3,\space 5,\space 8,\space 13,\space 21, \space34, …}$$
a.   Describe the pattern that you notice. How is each next term determined?
b.   This pattern is famously called the Fibonacci sequence. Write a recursive formula to represent the Fibonacci sequence. Write a formula in sequence notation using
$${a_n}$$
and in formula notation using
$${f(n)}$$
.
c.   If
$${a_{15}=610}$$
and
$${a_{16}=987}$$
, what are the values of
$${a_{17}}$$
and
$${a_{14}}$$
?
Problem 2
For each sequence below, write a recursive formula, in both sequence notation and function notation, to represent the sequence.
a.
$${18,\space 13,\space 8,\space 3,\space -2,\space …}$$
b.
$${4,\space 12,\space 36,\space 108,\space 324,\space …}$$
Problem 3
A sequence is given by an explicit formula, as shown below, where
$$n$$
represents the term number.
$$a_n=4n-1$$
for
$$n\geq1$$
a.   Write the first five terms in the sequence.
b.   Write a recursive formula to represent the sequence.


correct_option_index: 2

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