To determine the correct equation of the square root function that Rhianna graphed, we need to analyze the given options you provided:
- \( y = \sqrt{12x + 4} \)
- \( y = \frac{1}{2} \sqrt{x + 4} \)
- \( y = \sqrt{2x - 4} \)
- \( y = 2 \sqrt{x - 4} \)
- \( y = \sqrt{2x + 4} \)
- \( y = 2 \sqrt{x + 4} \)
- \( y = \sqrt{12x - 4} \)
Since the question states it is a square root function, we can focus on the functions that realistically represent a square root function.
To narrow it down, consider the general shape of square root functions, which typically start at a certain point (determined by the values under the square root) and increase.
The only functions that appear to conform to that basic characteristic are those where the expression under the square root is non-negative, leading to the understanding that there’s a domain restriction.
You would generally analyze the domain for functions like \( \sqrt{ax + b} \) or \( \sqrt{2x - 4} \):
- For \( \sqrt{2x - 4} \): The domain is \( x \geq 2 \).
- For \( 2 \sqrt{x - 4} \): The domain is \( x \geq 4 \).
- For \( \sqrt{12x - 4} \): The domain can be determined as \( x \geq \frac{1}{3} \).
However, without any additional context or graph from Rhianna’s work, we might focus on the linear transformation and shifts of the typical \( y = \sqrt{x} \) function to determine where it could be shifted.
If I were to make an educated guess based on the presented forms, options like \( y = 2 \sqrt{x - 4} \) or \( y = \sqrt{2x - 4} \) are promising due to their simpler expressions involving standard forms of square root functions.
Thus, the most plausible equations, keeping the attributes of square root functions in mind, would be either \( y = \sqrt{2x - 4} \) or \( y = 2 \sqrt{x - 4} \) which denote a basic square root transformation.
If you have further context or constraints, such as the shape of the graph or specific shifts or stretches, it would help narrow it down further!
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