The linear function f has a slope of 4. If g(x) = 3f(x) - 7, what is the slope of g?

Write $f(x) = 4x + c$ for some constant $c$. Then $g(x) = 3(4x + c) - 7 = 12x + 3c - 7$. The slope of $g$ is the coefficient of $x$, which is 12, choice D. Multiplying a function by 3 multiplies its slope by 3, while subtracting 7 only shifts the graph down and does not change the slope. Choice A (4) ignores the multiplication by 3. Choice B ($-7$) is the vertical shift, not the slope. Choice C (5) comes from adding $3 + 4 - 2$ or some combination, instead of multiplying: slope is scaled, not added to.