lessons > logarithmic functions > quiz - logarithmic functions\nwhich of the following is the graph of…

Explanation:

Step1: Analyze the transformation of the parent - function

The parent function of $y = \log(x)$ has a vertical asymptote at $x = 0$ and passes through the point $(1,0)$. For the function $y=\log(x - 1)-3$, the transformation $x\to x - 1$ shifts the graph of the parent - function $y = \log(x)$ 1 unit to the right, and the transformation $y\to y-3$ shifts the graph 3 units down. So the vertical asymptote of $y=\log(x - 1)-3$ is $x = 1$.

Step2: Check the key - points

When $x=2$, $y=\log(2 - 1)-3=\log(1)-3=0 - 3=-3$. So the graph passes through the point $(2,-3)$.

Answer:

(Without seeing all the options, we can't give a definite letter - answer. But based on the above analysis, the graph should have a vertical asymptote at $x = 1$ and pass through $(2,-3)$. If one of the options meets these criteria, that is the correct one.)