Shift the function and transform the key features of the graph. By translating the graph of the rational function, class members find out how the key features alter. Pupils determine the domain, range, asymptotes, and intervals of...

Find deeper meaning in graphs. Pupils use the knowledge gained from the previous sections in the unit to sketch graphs of a function's derivative. Learners also see how to sketch a graph of a function given the graph of its derivatives....

Pupils draw the graph of a door opening and closing over time. They graph a given function on their calculators, create a table of values and interpret the results by telling if the door is opening or closing and evaluate the average...

Get close to your favorite line. Scholars use end behavior to help find horizontal asymptotes. With the understanding of domains of rational functions, learners find vertical asymptotes and then use graphing calculators to verify the...

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...

Algebra II classes solve problems relating to piecewise functions, step functions, and decomposition/composition of functions. They utilize links to work with real world examples. Mr. Pleacher has added humor to the lesson by including...

Learners practice using their knowledge of how to interpret a function and use function notation. The activity includes two questions. Given an input of a function and its output, the first question asks learners to write the ordered...

Investigate the definition of inverse functions graphically. Using the interactive, scholars create a graph of a function and view its resulting inverse. They then determine whether a group of functions have inverses that are also...

They say a graph is worth a thousand points. The interactive allows users to graph a wide variety of functions and equations. Using the included keyboard or typing directly into the list, learners determine the graph of a function....

The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra lesson. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching notes and lots of...

Time to take a second look at derivatives finding concavity. While watching the video, learners find out the definition of concavity. Individuals see how to determine whether an interval is concave up or concave down using graphs and the...

In this calculus worksheet, learners solve problems using the first and second derivatives. They define the behavior of the function based on the derivative. There are 11 questions with an answer key.

Differentiate between calculus concepts. The beginning of a helpful calculus resource begins with a short review of functions and moves right into limits to define derivatives. The six-chapter resource continues with applications of...

If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...

Your AP Calculus learners probably have their ID numbers memorized, but have they tried graphing them? Pique your pupils' interest by asking each to create a unique polynomial function based on their ID numbers, and then analyze the...

Perform a switch to find the inverse of a parametric equation. Pupils match four parametric functions with the graph of the their inverses. Using the graphs, learners determine whether particular points are on the original parametric...

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...

Continue a study of calculus by using a slideshow to introduce the concept of continuity. After defining the term, the presentation provides examples of functions that are discontinuous and introduces different types...

Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...

Provide a review for the exam so individuals don't tank. AP® provides the free-response questions for teachers to use to help their pupils prepare for the exam. The six BC questions from 2007 include regions bounded by functions, water...

In this Pre-Calculus/Calculus worksheet, students graph polynomial functions, identifying the x- and y-intercepts as well as end behavior.  The two page worksheet contains sixty problems.  Answers are included. 

Let's see what the class learned! The last installment of the 23-part Pre-calculus module consists of nine assessment questions designed to measure a specific portion of a standard in the unit. Learners demonstrate their understanding of...

What kind of functions have holes in their graphs? Here, the teacher guides the class on how to use the simplified function of a rational function to aid in the graphing of the original rational function. T-tables are used in order...

Does the point continually move along the graph? Pupils drag a line across two functions to determine whether they are continuous or not. They answer questions about the properties of continuous and discontinuous functions. Using their...