Questions: Fill in the table using this function rule. f(x) = √x + 2 Simplify your answers as much as possible. Click "Not a real number" if applicable. x f(x) -9 0 9 16

Fill in the table using this function rule.
f(x) = √x + 2

Simplify your answers as much as possible. Click "Not a real number" if applicable.

x f(x)
-9
0
9
16

Transcript text: Fill in the table using this function rule. \[ f(x)=\sqrt{x}+2 \] Simplify your answers as much as possible. Click "Not a real number" if applicable. \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline-9 & $\square$ \\ \hline 0 & $\square$ \\ \hline 9 & $\square$ \\ \hline 16 & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

To fill in the table using the function rule $ f(x) = \sqrt{x} + 2 $, we need to evaluate the function for each given value of $ x $. If $ x $ is negative, the square root is not a real number. For non-negative values of $ x $, compute the square root and add 2.

Step 1: Evaluate $ f(x) $ for $ x = -9 $

The function $ f(x) = \sqrt{x} + 2 $ involves taking the square root of $ x $. Since $-9$ is negative, $\sqrt{-9}$ is not a real number. Therefore, $ f(-9) $ is not a real number.

Step 2: Evaluate $ f(x) $ for $ x = 0 $

For $ x = 0 $, we have: \[ f(0) = \sqrt{0} + 2 = 0 + 2 = 2 \]

Step 3: Evaluate $ f(x) $ for $ x = 9 $

For $ x = 9 $, we have: \[ f(9) = \sqrt{9} + 2 = 3 + 2 = 5 \]

Step 4: Evaluate $ f(x) $ for $ x = 16 $

For $ x = 16 $, we have: \[ f(16) = \sqrt{16} + 2 = 4 + 2 = 6 \]