properties of the natural log function the graph of ln(x) is shown at the left. what is the domain and range…

Explanation:

Step1: Recall domain of ln(x)

The natural - log function $\ln(x)$ is defined only for positive real numbers. So, the domain is the set of all $x>0$, which in interval notation is $(0,\infty)$.

Step2: Recall range of ln(x)

As $x$ approaches $0$ from the right, $\ln(x)\to-\infty$, and as $x\to\infty$, $\ln(x)\to\infty$. So the range is $(-\infty,\infty)$.

Step3: Recall asymptote of ln(x)

The function $\ln(x)$ approaches negative infinity as $x$ approaches $0$ from the right. So, the vertical asymptote is $x = 0$.

Answer:

Domain: $(0,\infty)$ Range: $(-\infty,\infty)$ Asymptote: $x = 0$