Question

what is the range of the function $y = \sqrt{x + 5}$?
\\( \circ \\) $y \geq -5$
\\( \circ \\) $y \geq 0$
\\( \circ \\) $y \geq \sqrt{5}$
\\( \circ \\) $y \geq 5$

Explanation:

Step1: Recall the range of square root function

The square root function \( \sqrt{u} \) (where \( u \) is an expression) has a range of \( y \geq 0 \) for all real numbers \( u \) such that \( u\geq0 \), because the square root of a non - negative number is always non - negative.

Step2: Analyze the given function \( y = \sqrt{x + 5}\)

For the function \( y=\sqrt{x + 5}\), the expression inside the square root is \( x + 5\). The domain of the function is determined by the condition \( x+5\geq0\) (i.e., \( x\geq - 5\)), but when we consider the range, we look at the output values of \( y\). Since the square root of any non - negative number (in this case, \( x + 5\) is non - negative for the domain of the function) is non - negative, the value of \( y=\sqrt{x + 5}\) will always be greater than or equal to \( 0\).

Answer:

\( y\geq0 \)