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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.

• 3810

Dynagraphs

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

• 2718

The Function Elevator

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

• 2726

Position and Piecewise Velocity

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

• 2636

Particle Motion1

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

• 2600

Particle Motion 2

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

• 2597

Perfect Shuffles

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

• 2540

Slider Template

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

• 2596

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.

• 2298
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