In the equation y=a(2)^(b(x-c))+d, we have 4 variables a, b, c, and d that can transform the function. Let's analyze each one:
1. Variable 'a' is the coefficient of the function. Any changes to 'a' are going to scale the function vertically. That is, if 'a' increases, the function stretches vertically, and if 'a' decreases, the function compresses vertically.
2. Variable 'b' modifies the rate of change in the function. When 'b' changes, this doesn't scale or shift the function vertically - it affects the slope or shape of the graph, causing the function to grow faster or slower.
3. Variable 'c' affects the horizontal shifts of the function. Changing 'c' will horizontally translate the function left or right, but it does not cause a transformation in the vertical direction (or “range”).
4. Variable 'd' is the constant term in the equation. When 'd' is increased or decreased, this shifts the function up or down along the y-axis. This is a vertical shift of the function.
Therefore, understanding how each component of the equation influences the graph, only a and d transform the range of an exponential function. Changes in 'a' correspond to vertical scaling, while changes in 'd' correspond to vertical shifting. The variables 'b' and 'c' affect the function's behavior, but not its range. Thus, the correct answers are 'a' and 'd'.