which of the following is a graph for f(x) = ln6x?
which of the following is a graph for f(x) = ln6x?
Answer
Explanation:
Step1: Recall properties of logarithmic function
The function (y = \ln(6x)) is a logarithmic - type function. The domain of (y=\ln(6x)) is (x>0) (since the argument of the natural - logarithm function (6x>0)). The general shape of the natural - logarithm function (y = \ln(x)) is a curve that increases slowly for positive (x) values, passes through the point ((1,0)) (when (x = 1), (y=\ln(6\times1)=\ln6\approx1.79)). As (x\to0^{+}), (y\to-\infty).
Step2: Analyze the graphs
The first graph has a vertical asymptote at (x = 0) and is increasing for (x>0), which is consistent with the properties of (y=\ln(6x)). The second graph is a straight - line (linear function), not a logarithmic function. The third graph has a domain that includes negative (x) values, which is not correct for (y=\ln(6x)). The fourth graph has a different shape and does not match the general form of a logarithmic function.
Answer:
The first graph (left - most graph)