To determine which equation represents the graph, let's analyze the provided options and compare them with the graph.

Steps:

1. Identify Key Features of the Graph:

   • The graph starts at $x = 2$ with a $y$-value of 0.
   • The graph increases gradually, typical of a square root function.
   • The graph is shifted horizontally to the right, indicating a transformation.

2. Analyze the Options:

   • Option 1: $f(x) = \sqrt{x + 2}$
     • This function shifts the graph to the left by 2 units.
   • Option 2: $f(x) = \sqrt{x} + 2$
     • This shifts the graph upwards by 2 units.
   • Option 3: $f(x) = \sqrt{x - 2}$
     • This shifts the graph to the right by 2 units.
   • Option 4: $f(x) = \sqrt{x} - 2$
     • This shifts the graph downwards by 2 units.

Conclusion:

The graph starts at $x = 2$ and the function that corresponds to this behavior is $f(x) = \sqrt{x - 2}$, which shifts the basic square root function $f(x) = \sqrt{x}$ to the right by 2 units.

So, Option 3: $f(x) = \sqrt{x - 2}$ is the correct answer.

Would you like more details on this problem or have any questions?

Here are 5 related questions to expand your understanding:

1. How do horizontal shifts affect the graph of a function?
2. How would the graph change if the function was $f(x) = \sqrt{x - 4}$?
3. What is the domain of the function $f(x) = \sqrt{x - 2}$?
4. How can you determine the range of a square root function?
5. What is the effect of a vertical shift on the graph of $f(x) = \sqrt{x}$?

Tip: For square root functions, the graph always starts at the point where the expression inside the square root becomes zero.