select the correct answer. which graph represents the function f(x)= -log(x - 1)+1? o a. o b.
select the correct answer. which graph represents the function f(x)= -log(x - 1)+1? o a. o b.
Answer
Explanation:
Step1: Determine the domain
For the function $y =-\log(x - 1)+1$, the argument of the logarithm must be positive. So $x-1>0$, which gives $x > 1$. The graph should not have any part for $x\leq1$. Option A has parts of the graph for $x < 1$, so it is incorrect.
Step2: Analyze the behavior of the logarithmic - function
The parent - function of $y =-\log(x - 1)+1$ is $y=\log x$. The negative sign in front of the logarithm reflects the graph of $y = \log x$ about the $x$ - axis. The $x-1$ inside the logarithm shifts the graph of $y =-\log x$ one unit to the right, and the $+ 1$ shifts the graph one unit up. As $x$ approaches $1$ from the right ($x\rightarrow1^{+}$), $y\rightarrow+\infty$. As $x$ gets larger, $y$ decreases. Option B has the correct domain ($x>1$) and the correct behavior of the function.
Answer:
B.