The function f is defined by f(x) = kx - 3. If the graph of f is perpendicular to the line y = 1/4x + 2, what is the value of k?

Perpendicular lines have slopes whose product is $-1$ (negative reciprocals). The line $y = \frac{1}{4}x + 2$ has slope $\frac{1}{4}$, so $k \cdot \frac{1}{4} = -1$, giving $k = -4$, choice D. Choice A (4) flips the fraction but not the sign. Choice B ($\frac{1}{4}$) is the same slope, which would make the lines parallel. Choice C ($-\frac{1}{4}$) changes the sign but not the fraction, giving a line that is a reflection and not perpendicular. For perpendicular lines, flip the fraction and change the sign.