Question

given the function below, fill in the table of values, use the table of values to graph the function, and then identify the function’s domain and range.
$y = \sqrt{x + 4} + 3$

Explanation:

Step1: Calculate \( x + 4 \) when \( x = -4 \)

Substitute \( x = -4 \) into \( x + 4 \), we get \( -4 + 4 = 0 \).

Step2: Calculate \( \sqrt{x + 4} \) when \( x = -4 \)

Substitute \( x = -4 \) into \( \sqrt{x + 4} \), we have \( \sqrt{-4 + 4} = \sqrt{0} = 0 \).

Step3: Calculate \( y = \sqrt{x + 4} + 3 \) when \( x = -4 \)

Substitute \( x = -4 \) into \( y = \sqrt{x + 4} + 3 \), we get \( \sqrt{-4 + 4} + 3 = 0 + 3 = 3 \).

Answer:

For \( x + 4 \): \( 0 \)
For \( \sqrt{x + 4} \): \( 0 \)
For \( y = \sqrt{x + 4} + 3 \): \( 3 \)