Final answer:
The equation indicates a horizontal translation to the right by 2 units and a vertical translation downward by 3 units. Accordingly, the correct answers are option c for the horizontal shift and option d for the vertical movement.
Step-by-step explanation:
The equation g(x)=3( 41 ) x−2 −3 indicates a function that has undergone translation. Here, we are dealing with two types of transformations - horizontal and vertical. Looking at the equation, the 'x−2' term signifies a horizontal translation and the '-3' at the end of the equation signifies a vertical translation. Specifically.
- The 'x−2' corresponds to a horizontal translation to the right by 2 units.
- The '-3' indicates a vertical translation downward by 3 units
The equation thus represents a function that is translated 2 units to the right (c. Horizontally to the right side of the coordinate system) and 3 units down (b. Vertically downward in the coordinate system). In this case, the correct answers from the provided options would be option c for the horizontal translation and option d for the vertical translation.