Use the following function rule to find \( f(0) \) \( f(x)=4(9)^{x}+9 \) \( f(0)=\square \)

To find \( f(0) \), we substitute \( x = 0 \) into the function rule: \[ f(0) = 4(9)^{0} + 9 \] Since any number raised to the power of 0 is 1, this simplifies to: \[ f(0) = 4(1) + 9 = 4 + 9 = 13 \] Thus, \( f(0) = 13 \). To check your work, it's always good to review the properties of exponents! Remember, \( a^0 = 1 \) for any non-zero number \( a \). It’s also fun to experiment with other values of \( x \) to see how the function behaves! If you substitute in \( x=1 \), you will find \( f(1) = 4(9)^1 + 9 = 36 + 9 = 45 \), showing a rapid increase in function output as \( x \) grows.