Question

Use the image to answer the question.

A coordinate plane reveals a curve.

Rhianna graphed a square root function. What is the equation of the function she graphed?

(1 point)
Responses

y=2x+4−−−−−√
y equals 2 Start Root x plus 4 End Root

y=12x+4−−−−−√
y equals Start Fraction 1 over 2 End Fraction Start Root x plus 4 End Root

y=12x−4−−−−−√
y equals Start Fraction 1 over 2 End Fraction Start Root x minus 4 End Root

y=2x−4−−−−−√
y equals 2 Start Root x minus 4 End Root
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Answer 1

To determine the correct equation of the square root function graphed by Rhianna, we need to analyze the potential options given.

The general form of a square root function is usually expressed as \( y = a \sqrt{x - h} + k \), where:
- \( a \) determines the vertical stretch or compression,
- \( (h, k) \) determines the horizontal and vertical shifts.

Based on the options provided, we'll look for a square root function that demonstrates these characteristics. However, without the actual image or graph, I can't pinpoint the specific shifts or stretches.

Considering the forms given, the only options presented with proper square root formatting are:

1. \( y = 2\sqrt{x + 4} \)
2. \( y = \frac{1}{2}\sqrt{x + 4} \)
3. \( y = \frac{1}{2}\sqrt{x - 4} \)
4. \( y = 2\sqrt{x - 4} \)

If you have any details about shifts or the direction of the curve's graph (e.g., opening direction, vertex position), I could assist better in identifying the correct equation. Based on the characteristics of square root functions:

- If the curve opens upwards and is centered around a positive shift or additional points above or below the x-axis, it would likely be one of the first two options (with positive shifts).
- If the curve has a vertex positioned at \( (4, 0) \), this leads us to conclude that functions 3 or 4 could be valid choices.

Please provide additional information or visual details from the graph for more precise identification.