Math Example--Rational Concepts--Graphs of Rational Functions: Example 6

Topic

Rational Functions

Description

This example demonstrates the graph of the rational function y = -1 / (6x + 2). The graph features a vertical asymptote at x = -1/3, shown with a dashed red line on the grid. Students are asked to graph the function and identify its vertical asymptote.

Rational functions are a crucial topic in algebra, involving fractions of polynomial functions. This collection of examples aids in teaching the topic by providing visual representations of various rational functions, allowing students to observe how changes in the function affect its graph. By examining multiple examples, students can recognize patterns and develop a deeper understanding of asymptotes and function behavior.

Exposure to multiple worked-out examples is essential for students to fully comprehend mathematical concepts. It enables them to encounter different scenarios, reinforces key ideas, and helps develop problem-solving skills. This repetitive exposure can increase confidence and enhance overall understanding of rational functions.

Teacher's Script

Let's examine this graph carefully. Notice how the negative sign in the numerator has flipped the graph compared to previous examples. The vertical asymptote is at x = -1/3, which can be found by solving 6x + 2 = 0. Observe how the function approaches negative infinity as x approaches -1/3 from the right, and positive infinity as x approaches -1/3 from the left. Understanding these nuances and how they relate to the function's equation is key to mastering rational functions.

For a complete collection of math examples related to Rational Functions click on this link: Math Examples: Graphs of Rational Functions Collection.