Write a rational function with no vertical asymptotes and no holes. explain.

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)