QuestionApril 14, 2026

6. Which function results in a reflection over the y-axis? A) g(x)=sqrt (-x) B) g(x)=-sqrt (x) C) g(x)=sqrt (x-1) D) g(x)=-1sqrt (-x)

6. Which function results in a reflection over the y-axis? A) g(x)=sqrt (-x) B) g(x)=-sqrt (x) C) g(x)=sqrt (x-1) D) g(x)=-1sqrt (-x)
6. Which function results in a reflection over the y-axis? A) g(x)=sqrt (-x) B) g(x)=-sqrt (x) C) g(x)=sqrt (x-1) D) g(x)=-1sqrt (-x)

Solution
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Answer

A) g(x) = \sqrt{-x} Explanation 1. Recall reflection rule Reflection over the y-axis replaces x with -x in the function: g(x) = f(-x). 2. Check each option A) \sqrt{-x} → x replaced by -x → reflection over y-axis ✔ B) -\sqrt{x} → negative outside affects y-values, not x → no ✔ C) \sqrt{x-1} → shift, no reflection. D) -1\sqrt{-x} → same as -\sqrt{-x} → reflection over y-axis with vertical flip. 3. Identify correct match The simplest and direct reflection is option A.

Explanation

1. Recall reflection rule<br /> Reflection over the y-axis replaces $x$ with $-x$ in the function: $g(x) = f(-x)$.<br />2. Check each option<br /> A) $\sqrt{-x}$ → $x$ replaced by $-x$ → reflection over y-axis ✔ <br /> B) $-\sqrt{x}$ → negative outside affects y-values, not x → no ✔ <br /> C) $\sqrt{x-1}$ → shift, no reflection. <br /> D) $-1\sqrt{-x}$ → same as $-\sqrt{-x}$ → reflection over y-axis with vertical flip. <br /><br />3. Identify correct match<br /> The simplest and direct reflection is option A.
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