Question

fill in the table of values for the function (f(x) = \log_{5}(x) + 3). enter dne if the answer does not exist.

\

$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline 0 & \\\\ \\hline 1 & \\\\ \\hline 5 & \\\\ \\hline \\end{array}$$

graph the function by first placing the vertical asymptote:

Explanation:

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

$$f(0) = \log_{5}(0) + 3 \implies \text{DNE}$$

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

$$f(1) = \log_{5}(1) + 3 = 0 + 3 = 3$$

Step3: Evaluate the function at \(x = 5\)

$$f(5) = \log_{5}(5) + 3 = 1 + 3 = 4$$

Step4: Determine the vertical asymptote

$$x = 0$$

Answer:

For the table of values:

\(x\)	\(f(x)\)
1	3
5	4

For the graph:

• Vertical asymptote: \(x = 0\) (the y-axis)
• Key points to plot: \((1, 3)\) and \((5, 4)\)