Final answer:
The student’s question describes a transformation of the parabolic function f(x) = x^2 into a horizontal line at y=20, indicating a vertical translation of the graph upward by 20 units. This transformation changes the graph into a completely different function, which suggests it is not a simple modification of the original parabola.
Step-by-step explanation:
If we have a graph that is the result of transforming the function f(x) = x2, we must observe the changes in the graph's appearance compared to the original parabola. To identify the transformations that occurred, we look for changes in orientation, position, width, and steepness.
For a horizontal line
f(x) = 20
this indicates that the graph is now a horizontal line at y=20, which is a transformation known as translation. Since the value of f(x) does not change as x varies between 0 and 20, the line is horizontal suggesting that there has been a vertical shift or translation of the graph upward by 20 units. There is no squaring of x involved, and thus, no resemblance to the original parabola shaped graph of f(x) = x2. This transformation is very different from typical transformations such as shifts, stretches, or reflections. It suggests we are looking at a completely different kind of function rather than a transformed version of f(x) = x2.