To analyze the transformation from \( f(x) = 4x - 5 \) to \( f(x) = 4 \cdot 2x - 5 \), we can express it in terms of \( f(x) = 4 \cdot 2^x - 5 \).
In this case, \( k \) refers to the base of the exponential function, which is \( 2 \).
Next, to understand whether the graph shows a stretch or a compression, we consider the factor of \( 2 \) multiplying \( x \). When a function has a factor of \( k > 1 \) multiplying \( x \) (in this case, \( k = 2 \)), it results in a horizontal compression of the graph by a factor of \( \frac{1}{k} \) (i.e., it compresses the graph towards the y-axis).
Thus, the correct answer is:
2; compression.