Question

what is the domain of the square root function graphed as shown?
$x \geq -1$
$x \leq -1$
$x \leq 0$
$x \geq 0$

Explanation:

Step1: Recall square root domain

The square root function \( y = \sqrt{x} \) has domain \( x \geq 0 \) (since we can't take square root of negative numbers in real numbers). For a graphed square root function (assuming it's the basic or shifted appropriately, but the standard square root function's domain is \( x \geq 0 \)).

Step2: Evaluate options

• \( x \geq -1 \): Not standard square root domain (unless shifted, but no info of shift here, and standard is \( x \geq 0 \)).
• \( x \leq -1 \): Invalid, as square root of negative (for \( x < 0 \)) is not real.
• \( x \leq 0 \): Invalid, same as above (for \( x < 0 \), square root not real).
• \( x \geq 0 \): Matches the domain of the basic square root function \( y = \sqrt{x} \), where \( x \) must be non - negative.

Answer:

\( x \geq 0 \) (the option with \( x \geq 0 \))