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Which function would be produced by a horizontal stretch of the graph of \newliney=xy=\sqrt{x} followed by a reflection in the \newlinexx-axis?\newliney=2(−x)y=\sqrt{2(-x)}\newliney=−2xy=-\sqrt{2x}\newliney=(12)(−x)y=\sqrt{\left(\frac{1}{2}\right)(-x)}\newliney=−(12)xy=-\sqrt{\left(\frac{1}{2}\right)x}

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Q. Which function would be produced by a horizontal stretch of the graph of \newliney=xy=\sqrt{x} followed by a reflection in the \newlinexx-axis?\newliney=2(−x)y=\sqrt{2(-x)}\newliney=−2xy=-\sqrt{2x}\newliney=(12)(−x)y=\sqrt{\left(\frac{1}{2}\right)(-x)}\newliney=−(12)xy=-\sqrt{\left(\frac{1}{2}\right)x}
  1. Horizontal Stretch Effect: Understand the effect of a horizontal stretch on y=xy = \sqrt{x}. A horizontal stretch by a factor of 22 would replace xx with (1/2)x(1/2)x in the function, resulting in y=(1/2)xy = \sqrt{(1/2)x}.
  2. Reflection in x-axis: Apply the reflection in the x-axis to the stretched function. Reflecting y=(12)xy = \sqrt{\left(\frac{1}{2}\right)x} in the x-axis changes yy to −y-y, so the new function becomes y=−(12)xy = -\sqrt{\left(\frac{1}{2}\right)x}.

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