Work Step by Step
First, see figure 5.3, the graph of g(x)=ln(x). (The parent function) Note the shape and a characteristic point (1,0) on the graph (ln1=0). The graph of the function $g(-x)$ is obtained by reflecting the graph of the parent function g(x)=ln(x) across the y-axis. (As a result, the graph passes through $(-1,0)$ instead of (1,0)). Next, the graph of $-g(-x)$ is obtained from $g(-x)$ by reflecting it over the x-axis. So, the graph of $f(x)=-\ln(-x)$ passes through ($-1,0)$ instead of $(1,0)$, "flipped" over the x-axis... ... graph (c).