Question

choose the graph of (y = \log_{3}(x) - 3)

Explanation:

Step1: Identify the vertical asymptote

The domain of \(y = \log_3(x) - 3\) is \(x > 0\), which gives a vertical asymptote at \(x = 0\).

Step2: Calculate key points

Evaluate the function at \(x = 1\) and \(x = 3\):

$$y(1) = \log_3(1) - 3 = 0 - 3 = -3$$

$$y(3) = \log_3(3) - 3 = 1 - 3 = -2$$

Step3: Match with the correct graph

The top-left graph has a vertical asymptote at \(x = 0\) and passes through \((1, -3)\) and \((3, -2)\).

Answer:

The top-left graph.