Answer
Domain: $(0,\infty)$.
Range: $\mathbb{R}$
Graph:
Work Step by Step
The graph of this function is obtained from $ f_{1}(x)=\ln x$
by vertically stretching it by factor 2,
AND
reflecting it about the x-axis.
...Graphing $ f_{1}(x)=\ln x$ with a dashed line,
... The base is $e\approx 2.718\gt 1$, so the graph rises on the whole domain.
... Asymptote is the y-axis.
... As x gets near 0 from the right, the graph nears but does not cross the asymptote.
... The graph passes through the points
... $(\displaystyle \frac{1}{e},-1),(1,0),(e,1),(e^{2},2)$, and so on.
... Plot these points and join with a smooth curve.
Then, for each of the points used for graphing $f_{1}$,
double their y-coordinates and change their sign (vertically stretch and reflect)
plot the new points,
and join with a smooth curve (red on the image).
The asymptote remains the $y$-axis.
Domain: $(0,\infty)$.
Range: $\mathbb{R}$
