Answer
Domain = $\mathbb{R}$,
Range = $\mathbb{R}$.
Work Step by Step
$f(x)=2x+1$
is a linear function whose graph is a line. We need two points.
$x=0$ $\Rightarrow$ $y=1$ ... (0,1)
$x=1 \Rightarrow y=3$ ... (1,3)
Plot the points and connect with a straight line.
Domain = $\mathbb{R}$,
Range = $\mathbb{R}$.