Answer
Domain: $\mathbb{R}$.
Range: $(2,\infty)$
Graph:
Work Step by Step
The graph of this function is obtained from $f_{1}(x)=e^{x}$,
by raising it up by $2$ 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, raise each of the points used for graphing $f_{1}$
up by 2 units,
and join with a smooth curve (red on the image).
The asymptote is also raised by 2 units.
Domain: $\mathbb{R}$.
Range: $(2,\infty)$
