Question

1. use a graphing calculator or graphing utility to explore the graphs of $ln x$ and $ln(x - 1)$.label the following graph:$f(x) =$$g(x) =$a. $ln x$b. $ln x - 1$c. $ln x + 1$d. $ln(x - 1)$e. $ln(x + 1)$

Explanation:

Step1: Identify $f(x)$ via x-intercept

The x-intercept of $f(x)$ is $(1,0)$. Substitute $x=1$ into $\ln x$: $\ln(1)=0$, which matches.

Step2: Identify $g(x)$ via x-intercept

The x-intercept of $g(x)$ is $(2,0)$. Substitute $x=2$ into $\ln(x-1)$: $\ln(2-1)=\ln(1)=0$, which matches.

Step3: Verify horizontal shift

The graph of $g(x)$ is $f(x)$ shifted right 1 unit, which aligns with the transformation of $\ln x$ to $\ln(x-1)$.

Answer:

$f(x) =$ a. $\ln x$
$g(x) =$ d. $\ln(x-1)$