SUMMARY
The function $$y=\frac{ln(x-5)}{x}$$ has a vertical asymptote at $$x=5$$ due to the natural logarithm being undefined for values less than or equal to 5. Additionally, there is no vertical line at $$x=0$$ because the function approaches this line but does not become undefined there. The discussion clarifies that the logarithmic function's domain restricts it to values greater than 5, confirming that $$x=0$$ does not create a vertical asymptote.
PREREQUISITES
- Understanding of logarithmic functions and their domains
- Knowledge of vertical asymptotes in rational functions
- Familiarity with limits and continuity in calculus
- Basic algebraic manipulation of functions
NEXT STEPS
- Study the properties of logarithmic functions, particularly their domains
- Learn about vertical asymptotes and how to identify them in rational functions
- Explore limits and continuity, focusing on how they relate to asymptotic behavior
- Practice graphing functions with vertical asymptotes to visualize their behavior
USEFUL FOR
Students and educators in mathematics, particularly those studying calculus and function behavior, as well as anyone interested in understanding vertical asymptotes in logarithmic functions.