Final answer:
The function f(x) described as a horizontal line is neither one-to-one nor onto, therefore it is not a one-to-one correspondence for any interval of x.
Step-by-step explanation:
The question revolves around determining if a given function f(x), a mapping from real numbers to real numbers, is in fact a one-to-one correspondence, which means it must be both onto and one-to-one. We are given that f(x) is a horizontal line for the interval 0 ≤ x ≤ 20.
A horizontal line means the function has the same output for every input in the domain, thus, it cannot be one-to-one because different x values will have the same y value. Since it is not one-to-one, we can immediately conclude that it is not a one-to-one correspondence without even checking for it being onto. When graphing this function, it is clear that every x in the given interval maps to the same y, which does not cover all possible y values in the codomain of real numbers, further confirming it is not onto.