The given function is:

$y = \sqrt{-x + 3} - 1$

Let's break down this function to understand its characteristics and how it behaves on a graph:

1. Square Root Transformation: The basic function is $y = \sqrt{x}$, which has a starting point at (0, 0) and rises to the right as x increases. This graph is transformed in the following ways:

   • The negative sign inside the square root reflects the graph across the y-axis (i.e., the graph will be flipped horizontally).
   • The $+3$ inside the square root shifts the graph 3 units to the right.
   • The $-1$ outside the square root shifts the entire graph downward by 1 unit.

2. Behavior:

   • The domain of the function will be restricted by the square root, so we need $-x + 3 \geq 0$, which simplifies to $x \leq 3$.
   • The graph will start at the point $(3, -1)$ (since when $x = 3$, $y = 0 - 1 = -1$).
   • It will rise as we move left from $x = 3$, getting higher as $x$ decreases.

Now, let's match this behavior with the provided graphs:

• Graph A: The curve starts at the point $(-3, -1)$ and passes through $(-2, 0)$ and $(1, 1)$. This doesn't match the behavior of our function, since it starts at $x = 3$, not at $x = -3$.

• Graph B: The curve starts at $(-3, -1)$ and rises to the right. This does not match the function either because our curve starts at $x = 3$, not at $x = -3$.

• Graph C: The curve starts at $(3, 1)$, but the function should be starting at $(3, -1)$, so this doesn't match.

• Graph D: We don't have the description of graph D, but based on the other options, it appears to be the most likely candidate. However, without a direct look at graph D, this is speculative.

Conclusion:

• The curve should start at $(3, -1)$ and rise to the left. Based on the descriptions given, Graph B seems to be the closest match because it starts near $(-3, -1)$, but there is a need for further clarification or visual confirmation of graph D.

Would you like to clarify further or check the graphs on a calculator?