Combine functions for the first time. Pupils investigate composition of functions using a function table and then function machines in the 17th installment in a 23-part Precalculus series. Scholars learn the two notations for composition...

Understanding how functions transform is a key concept in mathematics. This introductory lesson makes a strong connection between the function, table, and graph when exploring transformations. While the resource uses absolute value...

Functions as inputs for other functions? After reviewing function notation and how to input values to evaluate functions, class members input functions into functions, essentially determining the composition of functions.

Making connections between a function, table, graph, and context is an essential skill in mathematics. Focused on comparing linear and exponential relationships in all these aspects, this resource equips pupils to recognize and interpret...

Collaborative learners will see the geometric addition of functions by graphing the sum of two graphed curves on the same coordinate plane. This task then naturally flows into giving learners the algebraic representation of the curves...

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...

Show your class members that if they can graph a linear function, they can graph an absolute value function. Groups create an absolute value graph using a table, then entertain the idea of an absolute value function defined as two...

Graphing by hand does have its advantages. The 19th installment of a 35-part module prompts pupils to use skills from previous lessons to graph exponential and logarithmic functions. They reflect each function type over a diagonal line...

Why is that graph wider? Pupils learn about stretching and shrinking graphs of square root, absolute value, cubic, and quadratic functions. They study both vertical and horizontal stretches and shrinks in addition to reflections. 

Undo the functions. Learners refresh their knowledge of inverses of functions from Algebra II in the 19th section of a 23-part Precalculus unit. Pupils look at inverses in tables and graphs. They then add to their understanding of...

Paper folding, flu spreading in a school, bacteria growth, and continuously compounded interest all provide excellent models to study exponential functions. This is a comprehensive resource that looks at many different aspects of...

Middle schoolers describe plotting functions on the Cartesian coordinate plane. They solve functions on paper and using an online tool to plot points on a Cartesian coordinate plane creating lines and parabolas.

Introduce a new type of function through discovery. Math learners build an understanding of rational expressions by creating tables and graphing the result. 

Seeing functions in nature is a beautiful part of mathematics by analyzing the motion of a dolphin over time. Then take a look at the value of a stock and maximize the profit of a new toy. Explore the application of quadratics by...

What do you get when you cross piecewise functions with transformations?  An engaging lesson! The conclusion of a four-part series on the transformations of functions asks class members to apply transformations to piecewise...

Does a linear or exponential model fit the data better? Guide your class through an exploration to answer this question. Pupils create an exponential and linear model for a data set and draw conclusions, based on predictions and the...

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...

Is there a relationship between powers and roots? Here is a lesson that asks individuals to examine the graphical relationship. Pupils create a table of values and then graph a square root and quadratic equation. They repeat the process...

Scholars learn what it means for a relation to be a function and see various representations of functions. After learning the definition, they participate in a card sorting activity classifying relations as functions or not.

What happens to a function whose graph is translated horizontally? Groups find out as they investigate the effects of addition and subtraction within a function. This nineteenth lesson in a 26-part series focuses on horizontal...

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...

Skeeters are used to model linear and exponential population growth in a wonderfully organized lesson plan including teachers' and students' notes, an assignment, graphs, tables, and equations. Filled with constant deep-reaching...

Practice graphing basic equations. Algebra learners complete a table showing values of x and y. They graph the results on a coordinate grid. There are six problems: three equations are linear, and three are quadratic. The "show your...

This interactive website provides a variety of lesson plans according to which standards you are applying and which textbook you use. Introduce functions to your class by having them construct single operation machines and create...