Matching rational functions to their graphs | Rational expressions | Algebra II | Khan Academy

TL;DR

This video analyzes three functions and their potential definitions by looking at their graphs and identifying vertical and horizontal asymptotes.

Transcript

Voiceover:So, we've got three functions graphed here. The function f in magenta. We have the function g in this green color. And we have the function h in this dotted purple color. And then we have three potential expressions, or three expressions that could be potential definitions, for f, g, and h. And what I want to do in this video, is try to m... Read More

Key Insights

• 🚥 Analyzing the graphs and identifying vertical and horizontal asymptotes can help match functions to their definitions.
• 😥 Vertical asymptotes indicate points where the function is undefined.
• 🚥 Horizontal asymptotes reveal the behavior of the function at infinity.
• ❓ Deductive reasoning can be used to eliminate potential definitions and match functions to their correct definitions.

Questions & Answers

Q: How does the speaker suggest matching the functions to their definitions?

The speaker suggests two approaches: analyzing the graphs and identifying the presence of vertical asymptotes or using deductive reasoning based on the behavior at specific points.

Q: How does the speaker determine the potential definition for function f?

Function f has a vertical asymptote at x = -5. By checking which potential definition is not defined at x = -5 and has a vertical asymptote at that point, the speaker determines the correct definition.

Q: How does the speaker differentiate between functions g and h?

Both g and h have a vertical asymptote at x = 5. However, by analyzing the horizontal asymptotes, the speaker matches the correct definition to function h, which has an asymptote at y = 2.

Q: How does the speaker confirm the horizontal asymptotes for functions f and g?

By looking at the behavior of the functions at infinity, the speaker confirms that function f approaches 1 and function g approaches -2. This aligns with the given horizontal asymptotes.

Summary & Key Takeaways

• The video discusses three functions (f, g, and h) and their potential definitions.

• The speaker suggests two approaches for matching the functions to their definitions: analyzing the graphs and identifying vertical and horizontal asymptotes.

• The speaker uses deductive reasoning to match the functions to their definitions based on the presence of vertical asymptotes and the behavior of the functions at infinity.