Horizontal and Vertical Asymptotes - Slant / Oblique - Holes - Rational Function - Domain & Range

TL;DR

This video explains how to identify and graph the vertical, horizontal, and slant asymptotes of rational functions.

Transcript

in this video we're going to focus on finding the horizontal and vertical asymptote of a rational function in addition we're also going to find the slant or oblique asymptote if it's there so let's begin let's go over our first function y is equal to one over x minus three to find the vertical asymptote set the denominator equal to zero so if we se... Read More

Key Insights

• 😫 Finding the vertical asymptote involves setting the denominator equal to zero.
• 🚥 Determining the horizontal asymptote depends on the degrees of the numerator and denominator.
• 😥 Graphing rational functions involves considering the behavior near asymptotes and test points on either side.
• 🧡 The domain is determined by removing the vertical asymptote, and the range by removing the horizontal asymptote.

Summary & Key Takeaways

• Vertical asymptotes can be found by setting the denominator equal to zero. The vertical asymptote for y = 1/(x-3) is x = 3.

• Horizontal asymptotes are determined by the degrees of the numerator and denominator. The horizontal asymptote for y = 1/(x-3) is y = 0.

• To graph the function, test points on either side of the asymptotes are used. For y = 1/(x-3), the graph is above the horizontal asymptote on the right side and below it on the left side.