Questions: Radicals and Quadratic Functions Table for a square root function Fill in the table using this function rule. f(x) = sqrt(3-x) Simplify your answers as much as possible. Click "Not a real number" if applicable. x f(x) -22 3 7

Radicals and Quadratic Functions Table for a square root function Fill in the table using this function rule. f(x) = sqrt(3-x) Simplify your answers as much as possible. Click "Not a real number" if applicable. x f(x) -22 3 7
Transcript text: Radicals and Quadratic Functions Table for a square root function Fill in the table using this function rule. \[ f(x)=\sqrt{3-x} \] Simplify your answers as much as possible. Click "Not a real number" if applicable. \begin{tabular}{|c|c|} \hline$x$ & $f(x)$ \\ \hline-22 & $\square$ \\ \hline 3 & $\square$ \\ \hline 7 & $\square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Evaluate \( f(-22) \)

Substitute \( x = -22 \) into the function \( f(x) = \sqrt{3 - x} \): \[ f(-22) = \sqrt{3 - (-22)} = \sqrt{3 + 22} = \sqrt{25} \] \[ \sqrt{25} = 5 \] Thus, \( f(-22) = 5 \).

Step 2: Evaluate \( f(3) \)

Substitute \( x = 3 \) into the function \( f(x) = \sqrt{3 - x} \): \[ f(3) = \sqrt{3 - 3} = \sqrt{0} \] \[ \sqrt{0} = 0 \] Thus, \( f(3) = 0 \).

Step 3: Evaluate \( f(7) \)

Substitute \( x = 7 \) into the function \( f(x) = \sqrt{3 - x} \): \[ f(7) = \sqrt{3 - 7} = \sqrt{-4} \] Since the square root of a negative number is not a real number, \( f(7) \) is not a real number.

Final Answer

The completed table is: \[ \begin{tabular}{|c|c|} \hline x & f(x) \\ \hline -22 & \boxed{5} \\ \hline 3 & \boxed{0} \\ \hline 7 & \text{Not a real number} \\ \hline \end{tabular} \]

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