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. 

Math is all about finding solutions and connections you didn't expect! Young mathematicians often first discover nonlinear patterns when graphing quadratic functions. The instructional activity begins with the vocabulary of a quadratic...

If you know one, you know them all! Parent functions all handle translations the same. This instructional activity examines the quadratic, absolute value, and square root functions. Pupils discover the similarities in the behavior of the...

Explore different types of functions using an interactive lesson. Learners enter functions and view the accompanying graphs. They can choose to show key features or adjust the scale of the graph.

The sky's the limit of what you create when combining functions! The module begins with a review of transformations of parent functions and then moves to combining different function types using addition, subtraction, and...

Sometimes there just isn't a parent function that fits the situation. Help scholars learn to combine function types through operations and compositions. Learners first explore a new concept with an introductory activity and then follow...

What is absolute value? What is an absolute value function? Emerging mathematicians solve equations containing variables inside an absolute value sign.  They graph each function on a coordinate plane and identify the maximum and...

Find relationships between the structure of a function and its graph. An engaging instructional activity explores seven parent functions and their graphs. Learners match functions to their graphs and describe transformations.

Efficiently graph a quadratic function using transformations! Pupils graph quadratic equations by completing the square to determine the transformations. They locate the vertex and determine more points from a stretch or shrink and...

Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...

Piece by piece ... dismantling a function can highlight interesting patterns. The task asks learners to slice functions in sections with the same vertical change. They then recreate the graph with these slices positioned horizontally....

Young mathematicians look for patterns in inverse functions as they relate to the original functions. The comprehensive lesson emphasizes vocabulary throughout as well as algebraic and graphical characteristics of the inverse functions.

Graphing doesn't need to be tedious!  When pupils understand key features and transformations, graphing becomes efficient. This lesson connects transformations to the vertex form of a quadratic equation. 

Take a unique approach to study the graphing of trigonometric functions. Young scholars consider two sine functions and write three functions that will lie between the two given. They use a graphing utility to assist in their explorations.

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...

Parent functions and their combinations create unique graphical designs. Learners explore these relationships with a progressive approach. Beginning with linear equations and inequalities and progressing to more complex functions,...

Learners explore the concept of sine and cosine.  In this sine and cosine lesson, students work in groups to graph sine and cosine functions.  Learners examine how coefficients in various parts of each parent function shift the...

Leaners investigate families of linear functions through dance. They choreograph dance moves to model nine unique linear functions of their choosing. Using their dance moves, teams create a video presentation complete with music and...

  Explore the connection between a finite graph, a directed graph, and a matrix. Graph lines and identify the relationship of matrices in real-world scenarios. Then use this information to work with a partner to plan and design a...

Students analyze function graphs.  In this Algebra II/Pre-calculus lesson, students investigate the graph of a function as they determine to which family of functions it belongs, determine the parent function and describe the...

Explore how real-world applications can be parabolic in nature and how to find quadratic functions that best fit data. A number of different examples of modeling parabolas are explored including a student scavenger hunt, the exploration...

Your young apprentices build a function describing the percent concentration of salt in a brine. The rational function is then related to the parent function, y= 1/x, and graphed. Finally, the apprentices predict the amount of fresh...

Learners use sliders to change the parameters of functions and examine how shifting parameters affects a graph. They identify the parameters of functions, find vertical and horizontal stretches, then calculate the scale factor and other...

Scholars investigate transforming parabolas.  In this transforming parabolas instructional activity, they take the parent graph y=x^2 and transform it by shifting left, right, up, and down and shrinking and stretching. The class...