Final answer:
The table highlights two asymptotes for the function f(x) = 1/x - 2: a vertical asymptote at x = 0 and a horizontal asymptote at y = -2. Dashed lines are drawn at these values to indicate the asymptotes which the function approaches but never crosses.
Step-by-step explanation:
To create a table highlighting the asymptote of the function f(x) = 1/x - 2, we must first understand what an asymptote is. An asymptote is a line that the graph of a function approaches but never touches. For the function f(x) = 1/x - 2, there are two asymptotes. The vertical asymptote occurs where the function is undefined, which is at x = 0 since division by zero is undefined. The horizontal asymptote is found by looking at the values of f(x) as x approaches infinity, which in this case is y = -2. Therefore, the table below highlights these asymptotes:
- Vertical Asymptote: x = 0
- Horizontal Asymptote: y = -2
When graphing the function, we can draw dashed lines at x = 0 and y = -2 to indicate where the asymptotes are located. The function approaches these lines but never crosses them. By recognizing these asymptotes, we can more accurately sketch the graph of the function.