Question

question 23 of 28
which of the following is the graph of ( y=log _{3} x - 1 )?

Explanation:

Step1: Analyze the parent function

The parent function of \(y = \log_{3}x-1\) is \(y=\log_{3}x\). The domain of \(y = \log_{3}x\) is \(x>0\), and it passes through the point \((1,0)\) since \(\log_{3}1 = 0\).

Step2: Consider the transformation

For the function \(y=\log_{3}x - 1\), it is a vertical - shift of the parent function \(y = \log_{3}x\). The transformation rule for \(y=f(x)+k\) (where \(k=- 1\) here) is a vertical shift. If \(k<0\), the graph of \(y = f(x)\) is shifted down by \(|k|\) units.
When \(x = 3\), \(y=\log_{3}3-1\). Since \(\log_{3}3 = 1\), then \(y=1 - 1=0\)

Answer:

B.