Question

which of the following functions is the reflection of the function \\(y = 2\sqrt{x}\\) across the x-axis?

\\(y = -2\sqrt{x}\\)
\\(y = \sqrt{x} - 2\\)

Explanation:

Identify the original function and transformation rule

The original function is:

$$ y = 2\sqrt{x} $$

A reflection across the \(x\)-axis of a function \(y = f(x)\) is given by:

$$ y = -f(x) $$

Apply the reflection rule to the function

Applying this transformation to the given function:

$$ y = -(2\sqrt{x}) = -2\sqrt{x} $$

Answer:

• (A) \(y = -2\sqrt{x}\) (Correct answer)
• (B) \(y = \sqrt{x} - 2\)