## Precalculus

### Functions and Graphs

This unit includes activities that treat functions in context, especially emphasizing rectilinear motion (position, velocity and distance traveled by an object moving in a straight line). A theme throughout the precalculus is the consideration of important families of functions, and this unit sets the stage for that treatment with the use of dynamic sliders to investigate the graphical effects of changing the parameters of a function.

### Precalculus: Functions and Graphs Activities

Title Type

#### Absolute Value

This lesson involves the family of absolute value functions of the form f(x) = a |x + c| + b.

• 3769

#### Dynagraphs

This lesson involves using a dynagraph to explore the relationship between the input and the output of a given function.

• 2702

#### The Function Elevator

This lesson involves creating and comparing graphical representations of position and velocity functions from a scenario.

• 2710

#### Position and Piecewise Velocity

This lesson involves creating and comparing graphical representations of velocity and position based on real-life scenarios.

• 2620

#### Particle Motion1

This lesson involves the motion of a particle along a straight, horizontal line.

• 2587

#### Particle Motion 2

This lesson involves the motion of a particle along a straight, horizontal line associated with a general position function.

• 2579

#### Perfect Shuffles

This lesson involves creating and using a composite function to describe certain ways of shuffling a deck of cards.

• 2530

#### Slider Template

In this activity, students learn to create a slider to use in various applications.

• 2586

#### The Classic Box Problem - Exploration

This lesson takes a classic optimization problem and uses the dynamic linking capabilities to visualize the problem in multiple representations: diagramatic, geometric, graphic, numeric.

• 2281