Final answer:
The transformation of f(x) = |x| to g(x) = 2[x] is best described as a vertical stretch. The graph of f(x) is V-shaped, while g(x) is a step function that increases by 2 for each integer value of x, showing each step height is twice that of the graph of f(x).
Step-by-step explanation:
The transformation of the graph of f(x) = |x| to the graph of g(x) = 2[x] involves a vertical stretch. For the function f(x) = |x|, the graph is a V-shaped graph with the vertex at the origin (0, 0). This reflects that the value of f(x) is equal to the absolute value of x, which means that it is equal to x when x is positive and equal to -x when x is negative. In contrast, the function g(x) = 2[x], where [x] denotes the greatest integer less than or equal to x (also known as the floor function), results in a step function that increases by 2 for each integer value of x.
Therefore, each step in the graph of g(x) has a height that is twice the corresponding height of the steps in the graph of the basic floor function. This means each value of [x] is multiplied by 2, which indicates a vertical stretch by a factor of 2 compared to the graph of f(x) = |x| if it were to be considered as a floor function (although |x| is not inherently a step function like [x]).