State whether there is a possible transformation of f in the form g(x) = f(x-k). where k is a constant, for which the graph of y = g(x) will have no x-intercepts. Justify your answer.

Answer 1

Yes, there is a possible transformation of f in the form g(x) = f(x-k) for which the graph of y = g(x) will have no x-intercepts. This is because if the original function f(x) has x-intercepts, then shifting the graph horizontally by k units to the right (i.e., g(x) = f(x-k)) will also shift the x-intercepts to the right by the same amount, and may move them completely out of the domain of the new function g(x). However, this is not necessarily guaranteed and depends on the properties of the original function f(x).