Math Example--Rational Concepts--Graphs of Rational Functions: Example 20

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = -(x - 3) / (x + 4). The graph features a vertical asymptote at x = -4, but it is incorrectly labeled as x = -2. Students are asked to graph the function and identify its vertical asymptote.

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

Exposure to multiple worked-out examples is crucial for students to fully grasp mathematical concepts. It allows them to encounter different scenarios, reinforces key ideas, and helps develop problem-solving skills. This repetitive exposure can boost confidence and enhance overall comprehension of rational functions.

Teacher's Script

Let's analyze this graph carefully. First, notice that there's an error in the labeling - the vertical asymptote is correctly located at x = -4, but it's mislabeled as x = -2. This is a good opportunity to remind students about the importance of careful analysis and not just accepting given information. The asymptote occurs where the denominator equals zero. Observe how the negative sign affects the graph's orientation. Pay attention to how the function approaches positive infinity as x approaches -4 from the right, and negative infinity as x approaches -4 from the left. Understanding these behaviors and how they relate to the function's equation is essential for 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.