The question asks you to identify the equation of $h(x)$ that represents the given graph.

Steps to Analyze:

1. Graph Overview:

   • The graph appears to resemble a square root function, which is typically of the form $y = \sqrt{x}$, but the curve is shifted.
   • The graph starts at $(1, 2)$, suggesting there is a transformation (translation) involved.

2. Transformation Details:

   • Shift in the x-direction: The graph does not start at $(0, 0)$, but at $(1, 2)$, implying a horizontal shift. If the function is in the form $y = \sqrt{x - h}$, the graph would shift horizontally by $h$.
   • Shift in the y-direction: The starting value of $y$ is 2 at $x = 1$, which suggests a vertical shift upwards by 2.

3. Checking the Answer Options: Based on the shifts described, the correct function should reflect both a horizontal shift by 1 and a vertical shift by 2. Thus, the equation will take the form: $h(x) = \sqrt{x - 1} + 2$

Correct Answer:

The equation that represents the graph is:

• $h(x) = \sqrt{x - 1} + 2$

Let me know if you would like a more detailed explanation or further questions related to this!

Here are 5 relative questions:

1. How do you identify vertical and horizontal shifts in square root functions?
2. What are the general transformations applied to a square root function?
3. How would the graph change if the equation was $h(x) = \sqrt{x + 1} + 2$?
4. What effect does multiplying the square root by a constant have on the graph?
5. How do you find the domain of the square root function $h(x) = \sqrt{x - 1} + 2$?

Tip: Always check the graph's starting point (domain) and shape when identifying transformations of root functions.