What's the rule that makes it true?  A virtual function machine generates output values as learners submit the input values. Their job is to analyze the inputs and outputs for a pattern and write a function rule.

Examine key features of various functions through exploration. A comprehensive lesson has learners describe the domain, range, end behavior and increasing/decreasing intervals of various functions. Function types include linear,...

Examine the connection between rational functions and their graphs. Individuals use an online manipulative to sort equations with horizontal and oblique asymptotes. They focus on the degree of the numerator and denominator.

Highlight the process of mathematical discovery for your classes. This lesson examines the development of the Fundamental Theorem of Calculus over time. Understanding the history of the theorem helps create a better understanding of the...

The Function That Shall Not Be Named? The eighth installment of a 35-part module uses a WhatPower function to introduce scholars to the concept of a logarithmic function without actually naming the function. Once pupils are...

Help learners discover the unique characteristics of the tangent function. Working in teams, pupils create tables of values for different intervals of the tangent function. Through teamwork, they discover the periodicity, frequency, and...

Take the work out of worksheets and use these problems and worked-out answer key as a resource. The problems reinforce skills in domain and range, identifying graphs, and even and odd functions.

Teach collaboration and communication skills in addition to graphing logarithmic functions. Scholars in different groups graph different logarithmic functions by hand using provided coordinate points. These graphs provide the basis for...

Find an easier way to double it. Using the price of an item and the Consumer Price Index, learners determine how long it will be for the price to double. Scholars calculate the length of time it would take for the price to double using a...

Continue the study of transformations with an examination of horizontal stretches, shrinks, and reflections. Individuals use the same process used in parts one and two of this series to examine horizontal changes. The resource also...

Curing cancer or finding the fountain of youth—the answer may be understanding the structure and function of telomeres. The relationship of telomeres to both aging and cancer have triggered aggressive research. A thorough lesson...

Even, odd, or neither? Pupils study even and odd functions using a well-balanced interactive. They determine whether a given function is even or odd from its graph.

How does the equation of a function reflect translations? Scholars manipulate the starting point of the parent square root function before determining the new equations that result from the translations. Class members also determine the...

Create a technical report explaining the components of a medical plan through a function. The project-based learning activity gives a medical insurance scenario that young mathematicians model using piecewise functions. Their analyses...

One-to-one means the answer is simple, right? Given four graphs, pupils use a vertical line to test each graph to find out if they are one-to-one. By using the resource, learners realize that not all one-to-one relations are functions....

How does a change in amplitude or period affect the equation of a sine function? Scholars move sliders to change the frequency and period of the sine function. The interactive displays the resulting equation, and pupils determine the...

Graphs are useful for many things, including seeing how much money you can make. Individuals create a graph of earnings from a job based on the number of hours. They determine the domain and range of the graph and answer challenge...

Create a shift in TV viewing habits. The interactive presents a cosine model of an individual's TV viewing habits during a year. Class members move the model to reflect given conditions. Finally, they determine key features from the...

Map your way to successfully understanding inverse functions. Pupils use an interactive map to investigate how changes in the graph of a function affect the graph of its inverse. The results of the activity lead to the conclusion that...

The form of a quadratic function paints a picture of its graph. Young mathematicians explore this connection by locating key features on a graph and then writing the corresponding equations. The interactive tutorial highlights key...

Provide a graphical view of inverses. Pupils manipulate points on a line and see the relationship of the graph with the graph of its inverse. Using the relationship between the graphs, scholars respond to questions concerning inverses...

How far is that boat from the lighthouse? Scholars create diagrams to represent a scenario given the angle of depreciation from a lighthouse to a boat. Learners apply the basic trigonometric functions to find various distances...

Two for one—create an invertible and non-invertible function from the same data. The task presents a function table with missing outputs for the class to use to create two functions. One of the functions should have an inverse while the...

Don't allow those polynomial functions to misbehave! Understand the end behavior of a polynomial function based on the degree and leading coefficient. Learners examine the patterns of even and odd degree polynomials and apply them to...