By Tricia Lobo
Updated Mar 24, 2022
A horizontal asymptote is the value that a function’s y‑coordinate approaches as x tends toward infinity. For example, the function y = 1/x approaches y = 0 as x → ∞. Instead of hand‑calculating limits, you can use your TI‑83 to generate a table of x and y values and observe the trend directly.
Navigate to the Y= screen and enter your function into Y1.
Press the Tbl button to set up a table. For a quick view of large x values, set TblStart to 20 and TblInc (table interval) to 20. Adjust these numbers if your function behaves differently at other ranges.
Display the table and scroll to higher x entries. Watch how y changes. If it steadily trends toward a constant—say, y = 1—then that constant is the horizontal asymptote. In this case, the asymptote would be y = 1.
This table‑based approach works for any rational or polynomial function and provides a visual confirmation of the asymptote without complex algebra.
