The linear function f has a slope of 6. If g(x) = f(2x), what is the slope of g?

Write $f(x) = 6x + c$. Then $g(x) = f(2x) = 6(2x) + c = 12x + c$. The slope of $g$ is 12, choice B. Replacing $x$ with $2x$ makes the graph change twice as fast, so the slope doubles. Choice A (6) assumes the inside change has no effect on the slope. Choice C (3) divides by 2, which would happen for $f\left(\frac{x}{2}\right)$. Choice D (8) comes from adding 2 to the slope rather than multiplying. Scaling the input scales the slope by the same factor.