1. The problem is to understand and graph the piecewise function given by $y=3x+3$ with the domain restriction $2 \le x \le 1$. 2. First, note that the domain $2 \le x \le 1$ is not valid because $2$ is greater than $1$. Usually, domain intervals are written with the smaller number first, so this might be a typo or mistake. 3. Assuming the intended domain is $1 \le x \le 2$, the function is $y=3x+3$ for $x$ in this interval. 4. The function $y=3x+3$ is a linear function with slope $3$ and y-intercept $3$. 5. To graph this function on the domain $1 \le x \le 2$, calculate the values at the endpoints: $$y(1) = 3(1) + 3 = 6$$ $$y(2) = 3(2) + 3 = 9$$ 6. So the graph is the line segment connecting points $(1,6)$ and $(2,9)$. 7. The function is continuous and increasing on this interval. 8. The Desmos latex for this piecewise function with domain restriction is: $$y=\left\{\begin{array}{ll}3x+3 & \text{if } 1 \le x \le 2 \\ \text{undefined} & \text{otherwise}\end{array}\right.$$