1. We are asked to find a linear function $f(x)$ such that $f(0) = 2$ and $f(2) = 4$. 2. A linear function has the form $$f(x) = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. Since $f(0) = 2$, substituting $x=0$ gives $$f(0) = m \cdot 0 + b = b = 2.$$ So, $b = 2$. 4. Next, use $f(2) = 4$ to find $m$: $$4 = m \cdot 2 + 2$$ $$4 - 2 = 2m$$ $$2 = 2m$$ $$m = \frac{2}{2} = 1$$ 5. Therefore, the linear function is $$f(x) = 1 \cdot x + 2 = x + 2.$$