Question

fill in the table of values for the function (f(x) = -6 log_{3}(x)). enter dne if the answer does not exist.

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$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline 0 & \\\\ \\hline 1 & \\\\ \\hline 3 & \\\\ \\hline \\end{array}$$

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graph the function by first placing the vertical asymptote:

Explanation:

Step1: Evaluate \(f(0)\)

$$f(0) = -6 \log_3(0) \implies \text{DNE}$$

Step2: Evaluate \(f(1)\)

$$f(1) = -6 \log_3(1) = -6 \cdot 0 = 0$$

Step3: Evaluate \(f(3)\)

$$f(3) = -6 \log_3(3) = -6 \cdot 1 = -6$$

Step4: Find vertical asymptote

$$x = 0$$

Answer:

For the table of values:

\(x\)	\(f(x)\)
1	0
3	-6

The vertical asymptote is at \(x = 0\).