the function $y = - 3sqrt{x - 6}$ is represented by graph

Explanation:

Step1: Analyze domain

For the function $y = - 3\sqrt{x - 6}$, the expression under the square - root must be non - negative. So $x-6\geq0$, which gives $x\geq6$. This means the graph starts at $x = 6$.

Step2: Analyze vertical stretch and reflection

The coefficient $-3$ in front of the square - root function means two things. First, the graph of $y=\sqrt{x}$ is vertically stretched by a factor of 3. Second, it is reflected about the $x$ - axis.

Step3: Match with graph

Among the given graphs, the one that starts at $x = 6$ and goes downwards (due to the negative sign) and has a steeper slope (due to the vertical stretch by a factor of 3) is the correct one.

Answer:

The graph that starts at the point $(6,0)$ and goes downwards with a steeper slope compared to the basic square - root function. (Since no specific labels for graphs like A, B, C are given in a way to directly choose an option, this is a descriptive answer based on the analysis). If there were labeled options like A, B, C etc., we would choose the one that matches the above description.