The range of the function \( f(x) = -(2)^x + 4 \) can be determined by analyzing the behavior of exponential functions.
For the given function:
\[ f(x) = -(2)^x + 4 \]
As \( x \) approaches positive infinity, \( 2^x \) grows without bound, and because of the negative sign in front, \( f(x) \) approaches negative infinity. As \( x \) approaches negative infinity, \( 2^x \) approaches zero, so \( f(x) \) approaches \( 4 \).
Thus, the range of the function \( f(x) \) is all real numbers greater than or equal to \( 4 \), or in interval notation: \( [4, \infty) \).
