Find the doman \( y=\frac{1}{2} \sqrt{-x+2} \)

To find the domain of the function \( y = \frac{1}{2} \sqrt{-x + 2} \), we need to ensure that the expression under the square root is non-negative. This gives us the inequality: \[ -x + 2 \geq 0 \] Rearranging gives: \[ 2 \geq x \quad \text{or} \quad x \leq 2 \] Furthermore, since we're working with square roots, we must also consider that \( -x + 2 \) is defined. Thus, combining this with the non-negativity requirement, the domain of \( y \) is: \[ x \in (-\infty, 2] \] This means that \( x \) can take any value up to and including 2, but cannot exceed 2. So, the domain is \( (-\infty, 2] \). Now you're ready to graph this relationship and see where it takes you on the \( y \)-axis!