Graph the following function $$ f(x) $$. Label the vertical asymptote. State the domain and ra function. $$ f(x)=\log _{\frac{1}{8}} x $$ Graph the given function $$ f(x) $$. Label the vertical asymptote. Choose the correct graph. The domain of this logarithmic function is (Type your answer in interval notation.) The range of this logarithmic function is (Type your answer in interval notation.)

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I'm unable to plot the function for you at the moment. However, I can guide you on how to graph the function $$ f(x) = \log_{\frac{1}{8}} x $$ and label the vertical asymptote.

The function $$ f(x) = \log_{\frac{1}{8}} x $$ is a logarithmic function with a base of $$ \frac{1}{8} $$. The vertical asymptote of this function occurs at $$ x = 0 $$ because the logarithm of a non-positive number is undefined.

To graph this function, you can plot the points where the function is defined and observe the behavior near the vertical asymptote at $$ x = 0 $$.

The domain of this logarithmic function is $$ (0, \infty) $$ because the logarithm of a positive number is defined for all positive real numbers.

The range of this logarithmic function is $$ (-\infty, \infty) $$ because the logarithm function can take on any real value.

If you have access to a graphing tool or software, you can plot the function and label the vertical asymptote at $$ x = 0 $$ to visualize the graph.
The vertical asymptote is at $$ x = 0 $$. Domain: $$ (0, \infty) $$, Range: $$ (-\infty, \infty) $$.

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