#### Answer

Answer choice $D$

#### Work Step by Step

The question is asking for the equation of the linear function in slope-intercept form, which is written as:
$f(x) = mx + b$
where $m$ is the slope, and $b$ is the value of $f(x)$ when $x = 0$.
The formula for the slope of a function is $\frac{\triangle f(x)}{\triangle x}$. The change in $x$ every time is $+1$. The change in $f(x)$ every time is $+2$. The slope is $2$.
$f(x) = 2x + b$
The value of $f(x)$ when $x=0$ is $1$, so the equation of this function is
$\boxed{f(x) = 2x + 1}$
The answer is $\boxed D$.