Fill in the table using this function rule. \[ f(x)=\sqrt{x}+5 \]

Sure! Let's fill in a table using the function rule: \[ f(x) = \sqrt{x} + 5 \] We'll choose a set of \( x \) values, compute \( \sqrt{x} \), and then add 5 to find \( f(x) \). | \( x \) | \( f(x) = \sqrt{x} + 5 \) | |--------|---------------------------| | 0 | \( \sqrt{0} + 5 = 0 + 5 = 5 \) | | 1 | \( \sqrt{1} + 5 = 1 + 5 = 6 \) | | 4 | \( \sqrt{4} + 5 = 2 + 5 = 7 \) | | 9 | \( \sqrt{9} + 5 = 3 + 5 = 8 \) | | 16 | \( \sqrt{16} + 5 = 4 + 5 = 9 \) | | 25 | \( \sqrt{25} + 5 = 5 + 5 = 10 \) | | 36 | \( \sqrt{36} + 5 = 6 + 5 = 11 \) | | 49 | \( \sqrt{49} + 5 = 7 + 5 = 12 \) | | 64 | \( \sqrt{64} + 5 = 8 + 5 = 13 \) | | 81 | \( \sqrt{81} + 5 = 9 + 5 = 14 \) | ### Explanation: 1. **Choose \( x \) Values:** Select non-negative values for \( x \) since the square root of a negative number is not a real number. 2. **Compute \( \sqrt{x} \):** Find the square root of each \( x \) value. 3. **Add 5:** Add 5 to the square root to get \( f(x) \). ### Graphical Representation: If you plot these points on a graph, you'll see that the function \( f(x) = \sqrt{x} + 5 \) is a square root function shifted upwards by 5 units. ### Example Calculation: For \( x = 16 \): \[ f(16) = \sqrt{16} + 5 = 4 + 5 = 9 \] Feel free to use different \( x \) values to populate more entries in the table as needed!