To determine the equation of the square root function that Rhianna graphed, we can look for the general form of a square root function, which is typically \( y = a\sqrt{x - h} + k \), where \( (h, k) \) is the vertex of the graph.
From the given responses, let's analyze them:
- \( y = \sqrt{12x - 4} \)
- \( y = \frac{1}{2} \sqrt{x - 4} \)
- \( y = \sqrt{2x + 4} \)
- \( y = 2 \sqrt{x + 4} \)
- \( y = \frac{1}{2} \sqrt{x + 4} \)
- \( y = 2 \sqrt{x - 4} \)
Only the functions that include the square root symbol are potential square root functions.
For example, the expressions inside the square root can give an idea of transformations applied to the basic function \( y = \sqrt{x} \).
Let's look at options that resemble \( y = a\sqrt{x} + k \):
- \( y = \frac{1}{2} \sqrt{x - 4} \) is a square root function with a vertical compression factor of \( \frac{1}{2} \) and shifted right by 4.
- \( y = 2 \sqrt{x + 4} \) has a vertical stretch by a factor of 2 and is shifted left by 4.
- \( y = 2 \sqrt{x - 4} \) has a vertical stretch by a factor of 2 and is shifted right by 4.
Without more information about the specific transformations or context of the graph, we cannot definitively identify which equation matches the graphed function. However, if a specific type of shift or transformation was expected from the function, it would lead us to the right choice.
If I had to provide a possible answer based on commonly known transformations, I'd suggest: \( y = \frac{1}{2} \sqrt{x - 4} \) (right shift by 4, vertical compression).
If there are specific characteristics from the graph that we can utilize to identify the right function, please share those, and we may be able to identify the correct equation more accurately!