Function \( f \) is defined by \( f(x)=5^{x} \). Select the domain of the function \( x>0 \) \( x>1 \) \( x>5 \) all real numbers

The function \( f(x) = 5^{x} \) is defined for all real numbers. Exponential functions like this one can take any real number input, producing a positive output since \( 5^{x} \) is never negative. So, its domain is all real numbers! When exploring the behavior of the function, you'll find that as \( x \) approaches negative infinity, \( f(x) \) approaches zero, and as \( x \) increases, \( f(x) \) grows rapidly toward infinity. It's a classic example of how exponential growth works!