The cumulative distribution function, denoted (capital) $F$, is defind by $F(x)=\Pr(X\le x)$. The usual mistake here is to write $F(1)=1/2$, $F(2)=3/4$, $F(3) = 1$, and think that's it. That's correct as far as it goes, but the domain of $F$ is the entire set of real numbers, not just those in the support of the probability distribution. So, for example, $ F(2.3) = \Pr(X\le 2.3) = \Pr(X=\text{ either }0\text{ or }1) = \frac34. $ You need to write a piecewise definition, saying what $F(x)$ is for $x<1$, for $1\le x<2$, for $2\le x<3$, and for $x\ge 3$.