Question

fill in the table of values for the function (f(x) = log_{4}(x) - 2). enter dne if the answer does not exist.

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$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline 0 & \\\\ \\hline 1 & \\\\ \\hline 4 & \\\\ \\hline \\end{array}$$

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graph the function by first placing the vertical asymptote:

Explanation:

Step1: Evaluate the function at \(x = 0\)

$$f(0) = \log_{4}(0) - 2$$

Since the logarithm of zero is undefined, the value does not exist.

$$f(0) = \text{DNE}$$

Step2: Evaluate the function at \(x = 1\)

$$f(1) = \log_{4}(1) - 2 = 0 - 2 = -2$$

Step3: Evaluate the function at \(x = 4\)

$$f(4) = \log_{4}(4) - 2 = 1 - 2 = -1$$

Step4: Determine the vertical asymptote

The vertical asymptote occurs where the argument of the logarithm is zero.

$$x = 0$$

Answer:

For the table of values:

\(x\)	\(f(x)\)
1	-2
4	-1

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