To analyze the given function $g(x) = -\sqrt{x - 5} - 3$:

Step 1: Break Down the Transformations

1. Square root function: The base function is $\sqrt{x}$.
2. Horizontal shift: The expression $x - 5$ indicates a horizontal shift 5 units to the right.
3. Reflection over x-axis: The negative sign outside the square root, $-\sqrt{}$, reflects the function across the x-axis.
4. Vertical shift: The subtraction of 3, $-3$, shifts the graph 3 units down.

Correct Answer:

• The correct transformation is Reflected over the x-axis.

Do you want a detailed explanation of each transformation?

Here are 5 related questions to expand your understanding:

1. How does the horizontal shift change if the function has $x + 5$ instead of $x - 5$?
2. What would happen to the graph if $g(x) = -\sqrt{x - 5} + 3$?
3. How can you identify a reflection over the y-axis in a function?
4. What happens to the graph if there is no negative sign before the square root?
5. What is the effect of adding 5 to $g(x)$ instead of subtracting 3?

Tip: Always identify transformations systematically: start with the base function and analyze shifts, reflections, and scaling.