let f(x) = 2^x and g(x) = -f(x - 1). Identify the transformations of f(x).
The transformation of f(x) involves a vertical reflection followed by a translation of one unit to the right.
- The vertical reflection is seen in the negative sign in front of g(x). This reflects the graph of f(x) across the x-axis.
- The translation of one unit to the right is seen in the "−1" inside the function g(x). This shifts the entire graph of f(x) to the right by one unit.
Therefore, the transformation of f(x) is a vertical reflection followed by a translation of one unit to the right.