Budding mathematicians graph given functions, identify the asymptotes, graph absolute values, and write a table of points. This three-page activity contains 23 problems.

In this graphs worksheet, students solve and complete 15 various types of problems. First, they determine the range of the function of the graph shown and write in interval notation. Then, students find the domain of the function in the...

Fifth graders analyze patterns and begin looking at function tables. This is a pertinent preparation for graphing patterns. In fact, consider giving your class a piece of graph paper and then teach them how!

Graph A goes with equation C, but table B. The short assessment task requires class members to match graphs with their corresponding tables, equations, and verbalized rules. Pupils then provide explanations on the process they used to...

Not all linear functions are linear transformations, only those that go through the origin. The third lesson in the 32-part unit proves that linear transformations are of the form f(x) = ax. The lesson plan takes another look at examples...

This activity begins with a review of linear functions and segues nicely over its fifteen examples and problems into a deep study of exponential functions. Linear and exponential growth are compared in an investment task. Data tables are...

Don't forget the tables! The previous lessons in this five-part series examined the linear equation and graph relationship. The current lesson adds tables to the mix. At completion, individuals should be able to create a table of values,...

In the activity on this webpage, learners use interactive graphing technology to investigate transformations of graphs. In the first part of the task, they look at the graph of a quadratic function with coordinates of a few points...

Use an activity to illustrate the different forms of a quadratic function. Here, the task asks learners to use composition of given functions to build an explicit function. The process emphasizes the impact of the order of...

Learners write an example to show a function statement true and another to show it false in this short task that addresses some common student misconceptions. 

This activity guides learners through an exploration of common transformations of the graph of a function. Given the graph of a function f(x), students generate the graphs of f(x + c), f(x) + c, and  cf(x) for...

Your learners can approach this task algebraically, geometrically, or both. They analyze the building of a linear function given two points and expand the concrete approach to the abstract when they are asked to find the general form of...

The equations look different, but their graphs are the same. How can that be? This activity leads your mathematicians in an exploration of three different forms of the same quadratic function. After comparing the equations, their graphs,...

Interpreting graphs of functions is addressed in a short instructional activity. Distance as a function of time is sketched on a graph, and a few quick questions ask about their meaning. This would make a good short assessment, or a nice...

In this exponential functions instructional activity, learners solve and complete 13 various types of problems. First, they define what is different and what is the same about exponential and linear functions. Then, students write a rule...

In this functions and integers worksheet, students combine positive and negative integers through addition, subtraction, multiplication and division. They complete function tables and graph the results of linear equations. This six-page...

For this exponential functions worksheet, students solve and complete 20 various types of problems. First, they graph the function and state the domain and range. Then, students tell whether the graph represents exponential growth or...

How long does it take alcohol to leave your system? Individuals explore this question by examining a polynomial function. They draw conclusions by analyzing the key features of the given polynomial function.

Through discussions and journaling, classmates determine methods to associate types of functions with data presented in a table. Small groups then work with examples and exercises to refine their methods and find functions that work...

What function will describe the insect population growth? Pairs or small groups work together to determine which type of function and specific function will model given scenarios. The scenarios differentiate between linear,...

Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...

Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...

Out of the swimming pool and into the math classroom! Young mathematicians analyze two linear functions representing the number of liters of water in a pool as it drains over time. They must evaluate functions, interpret function...

Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...