Answer
C.) 1
Explanation
Remember the rules for shifting functions:
\(f(x)+b\) shifts the function b units upward
\(f(x)-b\) shifts the function b units downward
\(f(x+b)\) shifts the function b units to the left
\(f(x-b)\) shifts the function b units to the right
Since we want tho shift \(f(x)=2^{x+4}\) 5 units to the right, we are using the rule: \(f(x-b)\) shifts the function b units to the right; in other words, we need to subtract 5 units to the input of the function:
\(f(x)=2^{x+4-5}\)
\(f(x)=2^{x-1}\)
But notice that there is already a negative sign in \(f(x)=2^{x-k}\), so to get \(f(x)=2^{x-1}\), k must be equal to positive 1.
