4. Practice completing the table of values for the given square root func Function: y=sqrt( )(x+3) mathbf(x) & -3 & -2 & 0 & 4 & 9 mathbf(y) & & & & &

We are tasked with completing the table of values for the given square root function \( y = \sqrt{x + 3} \). To do this, we will substitute each \( x \)-value into the function and calculate the corresponding \( y \)-value.<br /><br />## Step 1: Understand the function<br />The function is \( y = \sqrt{x + 3} \), which means that for any given \( x \), we add 3 to \( x \) and then take the square root of the result. The square root function is only defined for non-negative inputs, so \( x + 3 \geq 0 \).<br /><br />## Step 2: Calculate \( y \) for each \( x \)-value<br />### For \( x = -3 \):<br />Substitute \( x = -3 \) into the function:<br />\[<br />y = \sqrt{-3 + 3} = \sqrt{0} = 0<br />\]<br /><br />### For \( x = -2 \):<br />Substitute \( x = -2 \) into the function:<br />\[<br />y = \sqrt{-2 + 3} = \sqrt{1} = 1<br />\]<br /><br />### For \( x = 0 \):<br />Substitute \( x = 0 \) into the function:<br />\[<br />y = \sqrt{0 + 3} = \sqrt{3}<br />\]<br />This value cannot be simplified further, so it remains \( \sqrt{3} \).<br /><br />### For \( x = 4 \):<br />Substitute \( x = 4 \) into the function:<br />\[<br />y = \sqrt{4 + 3} = \sqrt{7}<br />\]<br />This value also cannot be simplified further, so it remains \( \sqrt{7} \).<br /><br />### For \( x = 9 \):<br />Substitute \( x = 9 \) into the function:<br />\[<br />y = \sqrt{9 + 3} = \sqrt{12} = 2\sqrt{3}<br />\]<br />Here, \( \sqrt{12} \) simplifies to \( 2\sqrt{3} \) because \( 12 = 4 \times 3 \), and \( \sqrt{4} = 2 \).<br /><br />## Step 3: Fill in the table<br />Now that we have calculated all the \( y \)-values, we can complete the table:<br /><br />\[<br />\begin{array}{|c|c|c|c|c|c|}<br\ />\hline<br\ />\ x\ \ &\ -3\ &\ -2\ &\ 0\ &\ 4\ &\ 9\ \\<br\ />\hline<br\ />\ y\ \ &\ 0\ &\ 1\ &\ \sqrt{3}\ &\ \sqrt{7}\ &\ 2\sqrt{3}\ \\<br\ />\hline<br\ />\end{array}<br />\]