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...

Do not cross the line while graphing. Provided with several coordinate axes along with asymptotes, pupils determine two functions that will fit the given restrictions. Scholars then determine other geometrical relationships of asymptotes...

Where do those asymptotes come from? Learners graph, simplify, and solve rational functions in the fifth module of a 10-part series. Beginning with graphing, pupils determine the key characteristics of the graphs including an in-depth...

They say it runs in the family. Small groups use a card sorting activity to group graphs of functions into families. After grouping by families, the class develops conclusions for parent functions and create a graphic organizer.

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...

There are an infinite number of reasons to use the resource. Scholars drag vertical and horizontal lines to the graph of a rational function to identify all asymptotes. They investigate the connection between asymptotes and limits to...

Limits can provide some valuable information about graphs. A slider interactive lets learners see the behavior of a graph around asymptotes. They investigate relationships between limits and asymptotes.

Rational functions become less mysterious when you know about limits. Individuals use an interactive to move a rational function on a coordinate plane and to investigate function values for certain x-values. They see how the limit...

Determining key features of a function is easy when you have a graph. Scholars sketch the graph of a rational function using technology. This graph helps in finding intercepts, asymptotes, and end behavior.

Patterns can be shifty! Find the pattern when shifting the graph of tangent. Pupils move the graph of tangent to different locations on the coordinate plane. They observe what happens to the function and its vertical asymptotes before...

Examine the connection between rational functions and their graphs. Individuals use an online manipulative to sort equations with horizontal and oblique asymptotes. They focus on the degree of the numerator and denominator.

Play with the graph of a rational function to discover the asymptote patterns. Young scholars use the interactive lesson to discover the relationship between the asymptotes and the function. As they manipulate the function, the graph...

Investigate exponential growth and decay. A set of six activities has pupils collecting and researching data in a variety of situations involving exponential relationships. They model these situations with exponential functions and solve...

Discover different patterns by making connections between a rational function and its graph. An engaging lesson plan asks scholars to explore the behavior of different rational functions. Groups discover a connection between the function...

Flip the script! Reverse the situation and ask the class to find the function given asymptotes. The task requires class members to use their knowledge of functions and asymptotes to create functions that have a given asymptote or...

Let's be rational about it. An instructive resource provides the definition of rational expressions and rational functions. Examples provide an explanation on how to determine excluded values from the domain. The resource continues to...

The slider feature on Desmos excellently shows how graphs change based on different variable values. Learners look at two similar rational functions and compare and discuss what happens when the numbers go from positive to zero to...

Graph the night away with all the different types of functions provided in the worksheet. Linear, quadratic, and rational all ask for graphs, domain and range and other key factors about the functions.

Sometimes graphing rational functions can feel a little "irrational." Starting with the basics, learners work their way through the pieces of these graphs and finish off with an application question. 

When developing intuition and skills for how graphs behave toward infinity, there is really no substitute for having the class get their hands dirty in graphing practice. This problem set with accompanying presentation and homework on...

In this video, Sal starts with the equation of a hyperbola by first comparing it to the equation of the circle, and ellipse. He then shows how to find the equation of the asymptotes by solving for y. He also shows a few intuitive ways to...

Continuing with the study of graphing hyperbolas, Sal shows an example of graphing a parabola that is centered at a point off the origin. By looking at the equation, first without shifting it, he helps listeners develop an intuitive...

Here is an example in this video of graphing a hyperbola centered at the origin. First, Sal shows solving for the equations of the asymptotes and then shows how to determine the direction of the hyperbola. He takes the approach of not...

Make a table to graph a rational equation. Make a list of values for x and plug them into the expression to get the y value. Then plot the ordered pairs on a graph. Hey, this graph looks funny! Something about asymptotes. Watch closely...