"The graph of y = g(t) is provided below.
Based on the graph, where is ln(g(x)) continuous?"
I did not include the graph but I would like to know in what ways does ln effect the continuity of a graph. Thanks.
since ln(g) is defined only where g>0, that will affect the continuity, I'm sure.
ah okay, thank you. That completely answers my prob.
To determine where ln(g(x)) is continuous based on the provided graph, we need to understand the effect of taking the natural logarithm (ln) on the continuity of a function.
The natural logarithm function, ln(x), is a continuous function for positive values of x. Therefore, ln(g(x)) will be continuous wherever g(x) is positive.
Here are some key points to consider:
1. Positive Values of g(x): ln(g(x)) is continuous wherever g(x) is positive because ln(x) is continuous for positive values of x. This means that if the graph of g(x) remains above the x-axis (i.e., positive values) for a certain interval, then ln(g(x)) will be continuous in that interval.
2. Non-positive or Zero Values of g(x): ln(g(x)) is undefined for g(x) ≤ 0 since the natural logarithm function is only defined for positive values. Therefore, if g(x) crosses or touches the x-axis (becomes non-positive or zero) at any point, then ln(g(x)) will not be continuous at that point.
In summary, ln(g(x)) is continuous wherever g(x) is positive, and it is not continuous wherever g(x) is non-positive or zero.
It would be helpful to consider the specific characteristics of the graph of g(x) to determine the intervals where ln(g(x)) is continuous. Without the visual representation of the graph, it is challenging to provide a more specific answer.