Not all continuous functions are differentiable. Pupils find three types of functions that are defined everywhere but not differentiable for all values of x. Along with providing examples of each type of function, students...

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...

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.

Weight is a function of the distance from sea level. Learners explore the many implications of this fact in an inquiry-based task. Given the function, pupils answer questions before manipulating the function to rewrite the distance...

How many intersections can two absolute value functions have? Young scholars consider the question and then develop a set of rules that describe the number of solutions a given system will have. Using the parent function and the standard...

Picture this—the class creates pictures using functions. Here, learners build functions to model specific graphic criteria. They use their knowledge of parent functions and transformations to create the perfect function. 

Examine and compare a linear and step function. The task provides two scenarios, one modeled by a linear function and the other a step function. Pupils create a graph for each and explain how each compares to the other.

How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...

Model the difference between the graphs of discrete and continuous functions. Scholars examine two scenarios and construct graphs to model the situation. They then compare their graphs that illustrate the subtle difference between these...

Transform your lesson for transforming functions. Scholars transform linear, quadratic, exponential, rational, and trigonometric expressions. They write their expressions to fit specific forms and identify the values of the resulting...

Find the function that fits. Scholars first identify the graph of a function that looks the same after a horizontal translation. They must then find the equation of a function whose graph lies only in two adjacent quadrants.

You can learn to graph as well as a calculator using calculus. The lesson introduces using derivatives to find critical points needed to graph polynomials. Pupils learn to find local maximums and minimums and intervals of increase...

The greater the latitude, the less of the Earth is north. Scholars graph the relationship between the latitude and the percentage of the Earth that is north of the latitude. Using the graph and the table, class members interpret values...

How old is the plant? Here is a task that presents the exponential decay function for carbon 14 in a plant. Pupils use the function to estimate the amount of carbon 14 in the plant when it died and analyze the function to find what...

Wheel the resource right into your classroom. Young mathematicians use given dimensions of a Ferris wheel to write a height versus time function. They use their functions to answer a set of questions about the Ferris wheel.

This performance task gives the population model of different types of flies and asks scholars to analyze the two populations. After interpreting the functions individually, participants compare the two populations and find the time...

Here is a study guide that breaks graphing quadratic functions into three simple steps. Quadratic functions in vertex and intercept form are included. Use during a lesson or afterward for skills practice. Note: Make sure your class has...

Your algebra learners will enjoy the real-life application of the three tasks presented here. They complete a table and a graph comparing the two options presented. One option is linear, while the other is exponential. After coming up...

In this composition functions worksheet, students solve 54 short answer problems.  Students find the composition of functions such as f of g and f + g.  Students find the domain of various functions.

In this algebra worksheet, 11th graders solve quadratic functions using the quadratic formula. They take the square roots of both side of each equation then graph both the linear and quadratic functions. There are a total of 84 problems...

In this differentiating special functions worksheet, students solve and complete 5 various types of problems. First, they differentiate each of the given functions. Then, students complete the table using a calculator and plot the points...

In this continuity and limits worksheet, students solve and complete 4 different types of problems. First, they determine which of the limits shown exist and then, evaluate them. They also find which functions are continuous at a given...

In this calculus worksheet, students identify functions based on different Theorems as it relates to calculus and the Fundamental Theorem. There are 13 questions dealing with differentiation and trigonometric graphs.

In this continuity worksheet, students solve 5 short answer problems about continuity.  Students determine where functions are continuous and find the limits of functions at points of discontinuity.