Final answer:
The rational function y = (1/(x+1))-7 has a vertical asymptote at x = -1 and a horizontal asymptote at y = -7. It has an x-intercept at x = -8 and a y-intercept at y = -7, but it does not exhibit even or odd function symmetry.
Step-by-step explanation:
For the rational function y = (1/(x+1))-7, this function exhibits key attributes such as a vertical asymptote at x = -1, where the function is undefined because, as described by OpenStax under the CC BY 4.0 license, the function approaches infinity as x approaches the value where the denominator is zero. There is also a horizontal asymptote at y = -7, considering that as x approaches infinity, the value (1/(x+1)) approaches 0, leaving y to approach -7. Unlike even or odd functions (where an even function is symmetric about the y-axis and an odd function exhibits point symmetry about the origin), this rational function does not exhibit symmetry but still has a defined x-intercept at x = -8 and a y-intercept at y = -7.