options: Build a function that models a relationship between two quantities.

Use functions to model relationships between quantities.

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

Build new functions from existing functions.

Understand the concept of a function and use function notation.

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

Prove and apply trigonometric identities.

Extend the domain of trigonometric functions using the unit circle.

Analyze functions using different representations.

Model periodic phenomena with trigonometric functions.

Construct and compare linear and exponential models and solve problems.

Define, evaluate, and compare functions.
problem_activity: Problem 1
Consider the three situations shown below.
$${|x|=5}$$
$${|x|<5}$$
$${|x|>5}$$
For each situation, let
$${{f(x)}=|x|}$$
and
$${{g(x)}=5}$$
. Graph each relationship between
$${f(x)}$$
and
$${g(x)}$$
in the coordinate plane and then use each graph to determine the solution to each situation.
Problem 2
Solve each absolute value inequality algebraically and verify the solution graphically.
a.
$${\left|x-{1\over2}\right|<3}$$
b.
$${\left|2x\right|>{7\over2}}$$
c.
$${\left|{1\over3}x\right|-4<-1}$$


correct_option_index: 5

8