Final answer:
The function that has y = -1 as an asymptote is y = x/(1-x), as it approaches y=-1 when x approaches positive or negative infinity.
Step-by-step explanation:
The student asks which function has y = -1 as an asymptote. An asymptote is a line that a graph approaches but never actually reaches. Functions with rational expressions often have asymptotes that are either horizontal, vertical, or oblique (slant). We look for a function where y approaches -1 as x approaches either positive or negative infinity.
Option (a) y = e⁻ʸ has a horizontal asymptote at y=0, not y=-1, as e to any power will always be positive. Option (b) y = -x/(1-x) has a vertical asymptote at x=1 and will not yield a horizontal asymptote at y=-1.
Option (c) y = ln(x+1) involves a logarithmic function which doesn't have a horizontal asymptote at y=-1. Option (d) y = x/(x+1) approaches y=1 as x goes to infinity, not y=-1. Finally, option (e) y = x/(1-x) indeed has a horizontal asymptote at y=-1, as when x becomes very large positive or negative, the fraction x/(1-x) approaches -1.