options: Model periodic phenomena with trigonometric functions.

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

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.

Analyze functions using different representations.

Prove and apply trigonometric identities.

Extend the domain of trigonometric functions using the unit circle.

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

Define, evaluate, and compare functions.

Construct and compare linear and exponential models and solve problems.
problem_activity: Problem 1
Below is the parent function of a quadratic function:
[IMG]
Given the equation in vertex form and the corresponding graph, identify the transformations to each function.
| **           Equation          ** |                             **           Graph          **                              | **           Transformation(s)          ** |
|-----------------------------------|-----------------------------------------------------------------------------------------|--------------------------------------------|
|       $${g(x)=(x+1)^2+3}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1b.png |                                            |
|       $${r(x)=-2(x-1)^2}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1c.png |                                            |
|        $${t(x)=(2x-1)^2}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1d.png |                                            |
Problem 2
A quadratic equation is
decreasing over the interval
$${-\infty < x < 3}$$
increasing over the interval
$${3 < x < \infty}$$
and has a rate of change of zero at
$${x=3}$$
.
Describe how each of the three graphs below fit this description.
| .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2a.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2b.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2c.png |
|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|


correct_option_index: 3

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