Final answer:
To determine the transformations from f(x) to g(x), consider translation, reflection, and dilation. Translation shifts the graph, reflection flips it across an axis, and dilation stretches or compresses the graph. Rotation, uncommon in function transformations, involves turning the graph.
Step-by-step explanation:
The functions f(x) and g(x) are related through transformations, which can include a translation, a reflection, a dilation, or, in rare cases, a rotation. For the function f(x), to determine the transformations required to obtain g(x), you should consider how the graph of g(x) is moved, stretched, flipped, or turned from the base function f(x).
A translation involves shifting the graph horizontally or vertically. If the function is given as f(x - d), the graph is translated d units in the positive x-direction. Conversely, f(x + d) implies a translation of d units in the negative x-direction. A reflection is noticed when the graph is flipped over an axis. If f(-x) is provided, for instance, this suggests a reflection over the y-axis.
Dilation is when the graph of the function is stretched or compressed. This can occur horizontally by changing the x-values or vertically by changing the y-values. Rotation, while not common in basic function transformations, would involve turning the graph around a fixed point.