options: Model periodic phenomena with trigonometric functions.

Analyze functions using different representations.

Define, evaluate, and compare functions.

Understand the concept of a function and use function notation.

Extend the domain of trigonometric functions using the unit circle.

Use functions to model relationships between quantities.

Construct and compare linear and exponential models and solve problems.

Prove and apply trigonometric identities.

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

Build new functions from existing functions.

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

Build a function that models a relationship between two quantities.
problem_activity: Problem 1
A rectangular garden has a width of
$$x$$
feet. The length of the garden is
$$4$$
feet longer than the width. Around the garden there is a pathway that measures
$$3$$
feet across the path.
[IMG]
The expression below represents the area of the pathway, not including the garden.
$$(x+6)(x+10)-x(x+4)$$
Explain what each part of the expression represents in context of the situation.
a.
$$x$$
b.
$$x+4$$
c.
$$x+10$$
d.
$$x(x+4)$$
e.
$$(x+6)(x+10)$$
Problem 2
An artist has a strip of wood
$$8$$
feet long to make a large rectangular picture frame. The possible dimensions of the frame that the artist can create can be represented as
$$x$$
and
$$4-x$$
, as seen in the diagram below.
[IMG]
What is the largest area the artist can frame with the
$$8$$
feet of wood?


correct_option_index: 1