The distance formula is

. In the ordered pairs (4, 6), the first number 4 represents the
x-coordinate while 6 is the
y-coordinate. In (7, -3), 7 is the
x-coordinate and -3 is the
y-coordinate. Substituting these coordinates results in

. Since subtracting a negative is equivalent to adding a positive, we now have
The function is applicable within the segments of x:
(-∞, -1) and [-1, 7), meaning it is valid for x < 7.
Importantly,
the function cannot be evaluated at x = -1 in the left part of the linear graph, while it is valid at x = -1 in the right segment of the same line. Additionally, the function is not defined at x = 7 or any value above it.
Conclusion: x < 7.