Final answer:
The graph of g(x) = f(x)3 results from vertically scaling the graph of f(x) = x² by a factor of 3. However, the vertex of the parabola remains unchanged; hence, none of the options A, B, C, or D accurately describe the transformation's effect on the graph's vertex.
Step-by-step explanation:
The question involves analyzing the effect of a transformation on the graph of a quadratic function. In this case, the original function is f(x) = x², which is a parabola with its vertex at the origin (0,0).
When we apply the transformation to create g(x) = f(x)3, we are essentially multiplying the output of f(x) by 3. Since f(x) is the same as y in the original function, this multiplication by 3 will scale the graph vertically by a factor of 3, but it does not move the vertex horizontally or vertically.
Therefore, all the y-values on the graph of f(x) are tripled to get the y-values for g(x). For example, if f(1) = 1, then g(1) = f(1)3 = 13 = 3. It is important to note that this transformation does not change the location of the vertex, only the steepness and the height at which any point (other than the vertex) is located on the graph.
In the transformation depicted, the vertex of graph g(x) does not move relative to the vertex of graph f(x), so none of the given options A, B, C, or D correctly describes the transformation. Therefore, no option is correct in this case.