options: Build new functions from existing functions.

Build a function that models a relationship between two quantities.

Prove and apply trigonometric identities.

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

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

Construct and compare linear and exponential models and solve problems.

Extend the domain of trigonometric functions using the unit circle.

Use functions to model relationships between quantities.

Analyze functions using different representations.

Model periodic phenomena with trigonometric functions.

Understand the concept of a function and use function notation.

Define, evaluate, and compare functions.
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: 8