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 raising it up by $3$ units.
Graph, with a dashed line, the graph of $f_{1}(x)=e^{x}$,
as instructed in the solution of exercise 47$:$
...Graphing $f_{1}(x)=e^{x}$ ,
... The base is $e\approx 2.718\gt 1$, so the graph rises on the whole domain.
... Asymptote is the x-axis.
... To the far left, the graph nears but does not cross the asymptote.
... The graph passes through the points
... $(-1,\displaystyle \frac{1}{e}),(0,1),(1,e),(2,e^{2})$, and so on.
... Plot these points and join with a smooth curve.
Then, for each of the points used for graphing $f_{1}$,
raise them up by $3$ units (add 3 to the y-coordinate)
plot the new points,
and join with a smooth curve (red on the image).
The asymptote remains the $y$-axis.
Domain: $(0,\infty)$.
Range: $\mathbb{R}$
