options: Use functions to model relationships between quantities.

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

Build new functions from existing functions.

Prove and apply trigonometric identities.

Extend the domain of trigonometric functions using the unit circle.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.

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

Build a function that models a relationship between two quantities.

Model periodic phenomena with trigonometric functions.

Analyze functions using different representations.

Understand the concept of a function and use function notation.
problem_activity: Problem 1
Given the graph below, over which interval is the average rate of change the greatest? Explain your reasoning.
[IMG]
a. Between
$${f(4)}$$
and
$${f(10)}$$
b.
$${10 \leq x \leq 15}$$
c. Between
$${(0,0)}$$
and
$${(4,11)}$$
d. From
$${x=0}$$
to
$${x=10}$$
Problem 2
The table below defines the relationship
$${y=f(x)}$$
.
Find the average rate of change from
$${f (0)}$$
to
$${f(5)}$$
.
|  $$x$$   | 0  | 0  | 4 | 5 |
|----------|----|----|---|---|
| $$f(x)$$ | 26 | 17 | 5 | 1 |
Problem 3
You leave from your house at 12:00 p.m. and arrive to your grandmother’s house at 2:30 p.m. Your grandmother lives 100 miles away from your house.
What was your average speed over the entire trip from your house to your grandmother’s house?


correct_option_index: 7

11