Rational functions are essential parts of the math curriculum, and understanding them is crucial in advanced math classes. Rational functions are the ratio of two polynomial functions. They can take many forms, including linear, quadratic, cubic, and higher-order functions. Teaching these functions can be challenging, as students must be able to identify the asymptotes and excluded values. However, with the right activities, teachers can make this topic easier and more compelling for students.
Activity 1: Asymptotes
Asymptotes are an essential feature of rational functions. An asymptote is a line that a curve approaches but never touches. When graphing rational functions, there can be three kinds of asymptotes: vertical, horizontal, and slant. To help students understand asymptotes better, we can use the following activity.
First, we can provide students with a set of rational functions to analyze and graph. After they have graphed the functions, we can ask them to identify the type of asymptote. Students can also identify the location of the asymptote, its equation, and the behavior of the function as it approaches the asymptote.
As an extension activity, teachers can ask students to create their own rational functions and graph them. They can also identify the asymptote type, equation, location, and behavior.
Activity 2: Excluded Values
Excluded values are numbers that are not defined in a rational function. They usually occur when the denominator of a rational function equals zero. Students often struggle with understanding excluded values, such as why they cannot divide by zero. However, teachers can use the following activity to help students make sense of excluded values.
The activity involves creating a “catch the ball” activity, where students throw a ball to each other while calling out an excluded value. For example, if the rational function is y = 1/(x-2), we can explain that the excluded value is x =2. The student with the ball must call out the excluded value before they pass the ball to another student. This activity can help students understand why we cannot divide by zero and the importance of excluded values.
As an extension activity, teachers can give students a set of rational functions and ask them to identify and label the excluded values. Students can also explain why these values are excluded and graph the functions with their excluded values labeled.
Conclusion
Teaching rational functions, asymptotes and excluded values can be challenging, but the above activities can help students better understand these critical concepts. Teachers should tailor their activities to their students’ learning styles and provide ample practice opportunities to ensure mastery. By doing so, students will gain a better understanding of rational functions and develop the necessary skills for advanced math classes.
