The following function is defined for any value of x:
f (x) = lxl / (lxl + 1)
For this case, we observe that the denominator can never be zero because we are in the presence of an absolute value.
So, for example, for x = -1 we have the denominator is:
l-1l + 1 = 1 + 1 = 2
The domain of the function will then be:
x = (- inf, inf)
Answer:
a rational function with no vertical asymptotes and no holes is:
f (x) = lxl / (lxl + 1)