A vertical asymptote of a rational function can be determined by finding the values of x that make the denominator of the function equal to zero, because the function becomes undefined at these points.
Given the function f(x) = (1)/(x + 4) + 1, we can see that the denominator is (x + 4).
An equation to find a vertical asymptote is formed by setting the denominator equal to zero and solving for x.
So, we have the equation x + 4 = 0.
To solve for x, we subtract 4 from both sides of the equation:
x + 4 - 4 = 0 - 4,
which simplifies to x = -4.
Therefore, the vertical asymptote of the function is x = -4.