f(x)=ln(x+4), domain, range, graph, and its inverse  Summary and Q&A
TL;DR
The video explains how to find the domain, graph, range, and inverse of the function f(x) = Ln(x) + 4.
Questions & Answers
Q: How do you determine the domain of f(x) = Ln(x) + 4?
To find the domain, we set the inside of the logarithm function greater than 0, resulting in x > 4. So, the domain of f(x) is (4, infinity).
Q: What happens when the inside of the logarithm function is 0?
When the inside of the logarithm function is 0, such as in the case of Ln(0), the value is undefined. However, it indicates a vertical asymptote in the graph.
Q: How do you graph the function f(x) = Ln(x) + 4?
By selecting a few xvalues and solving for the corresponding yvalues, we can plot points on the graph. Connecting these points forms a curve, which approaches a vertical asymptote as x approaches 4.
Q: What is the range of the function f(x) = Ln(x) + 4?
The range of the function is from negative infinity to positive infinity, denoted as (infinity, infinity). This is because the graph approaches negative infinity as x approaches 4 and goes up towards positive infinity as x increases.
Summary & Key Takeaways

The video discusses finding the domain of the function f(x) = Ln(x) + 4 by setting the inside of the logarithm greater than 0.

It explains how to graph the function by selecting various xvalues and solving for corresponding yvalues.

The video also covers the range and asymptotes of the function, as well as finding the inverse by switching x and y and isolating y.