Question

1. use a graphing calculator or graphing utility to explore the graphs of $ln x$ and $-3ln x$. label the following graph: $f(x)$ $g(x)$ a. $ln x$ b. $-3ln x$

Explanation:

1. For $f(x)$: The function $\ln x$ increases as $x$ increases, grows slowly for large $x$, and approaches $-\infty$ as $x$ approaches 0 from the right. This matches the upward-trending curve labeled $f(x)$.
2. For $g(x)$: The function $-3\ln x$ is a vertical stretch and reflection of $\ln x$ over the x-axis. It decreases as $x$ increases, approaches $+\infty$ as $x$ approaches 0 from the right, which matches the downward-trending curve labeled $g(x)$. Both functions pass through $(1,0)$ since $\ln 1 = 0$ and $-3\ln 1 = 0$, which aligns with the graph.

Answer:

$f(x)$: b. $-3\ln x$
$g(x)$: a. $\ln x$