Final answer:
The transition from f(x) to g(x) is not a rotation but an increase in the slope from 1 to 3, while the y-intercept remains at 5, resulting in a steeper line that increases in the positive x direction of the coordinate system.
Step-by-step explanation:
The translation from f(x) = x + 5 to g(x) = 3x + 5 does not involve any rotation, whether clockwise or counterclockwise. Instead, this transformation represents a change in the slope of the linear function. In the transition from f(x) to g(x), the slope of the line has increased from 1 to 3 while the y-intercept remains constant at 5. This means the graph of g(x) will be steeper than the graph of f(x), but they will both intersect the y-axis at the same point (0, 5).
There is no movement up or down as the y-intercept remains the same. The change solely happens in the steepness of the line, which is referred to as 'increasing in the positive x direction of the coordinate system' as the slope becomes more positive.