Question

which of the following graphs have the same domain? choose three correct answers.
$y = \sqrt{x}$
$y = \sqrt{x + 4}$
$y = 4\sqrt{x}$
$y = \sqrt{x} + 4$

Explanation:

Step1: Find domain of \( y = \sqrt{x} \)

For square root, the expression inside must be non - negative. So \( x\geq0 \).

Step2: Find domain of \( y=\sqrt{x + 4} \)

Set \( x + 4\geq0\), then \( x\geq - 4 \).

Step3: Find domain of \( y = 4\sqrt{x} \)

For \( 4\sqrt{x}\), the expression inside the square root \( x\geq0 \).

Step4: Find domain of \( y=\sqrt{x}+4 \)

For \( \sqrt{x}\), we need \( x\geq0 \).

The functions \( y = \sqrt{x}\), \( y = 4\sqrt{x}\) and \( y=\sqrt{x}+4 \) have the domain \( x\geq0 \), while \( y=\sqrt{x + 4}\) has a different domain (\( x\geq - 4 \)).

Answer:

• \( y = \sqrt{x} \)
• \( y = 4\sqrt{x} \)
• \( y=\sqrt{x}+4 \)