To determine the correct equation of the square root function that Rhianna graphed, we need to consider the general form of a square root function, which is typically expressed as:
\[ y = a \sqrt{x - h} + k \]
where:
- \( a \) is a vertical stretch or compression,
- \( (h, k) \) is the translation of the graph in the x and y directions, respectively.
Based on the provided response options, we can analyze some potential characteristics. Here is a breakdown of the options:
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\( y = 2\sqrt{x - 4} \): This indicates a vertical stretch by a factor of 2, and the graph is shifted 4 units to the right.
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\( y = 2\sqrt{x + 4} \): This indicates a vertical stretch by a factor of 2, and the graph is shifted 4 units to the left.
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\( y = \frac{1}{2} \sqrt{x + 4} \): This indicates a vertical compression by a factor of 2, and the graph is shifted 4 units to the left.
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\( y = 12\sqrt{x + 4} \) and \( y = 12\sqrt{x - 4} \): These would indicate vertical stretches but the factor of 12 is a bit extreme and not typical.
Based on the general characteristics of square root functions, the correct answer typically depends on the specific shifts and stretches desired, but without more context about the transformations (such as whether the graph opens up or down, or is shifted left or right), the safest assumption is that:
- \( y = 2\sqrt{x - 4} \) is a necessary positive square root function with a right shift.
Thus, based solely on plausible commonality among square root graphs, it would likely be that \( y = 2\sqrt{x - 4} \).
1 answer