Horizontal asymptotes are the numbers that "y" approaches as "x" approaches infinity. For instance, as "x" approaches infinity and "y" approaches 0 for the function "y=1/x" -- "y=0" is the horizontal asymptote. You can save time in finding horizontal asymptotes by using your TI-83 to create a table of "x" and "y" values of the function, and observing trends in "y" as "x" approaches infinity.
Access the "Y=?" part of your calculator, and input the function into "Y1."
Make a table to determine the behavior of the function as "x" approaches infinity. Click on the "Tbl" button. You may set "TblStart" to 20, and the table intervals to 20.
Display the table, and scroll through the values as "x" gets bigger and bigger. Determine any trends in "y" that occur. For instance, "y" may slowly and infinitesimally trend towards the number 1. If this is the case, then the horizontal asymptote is "y=1."
About the Author
Tricia Lobo has been writing since 2006. Her biomedical engineering research, "Biocompatible and pH sensitive PLGA encapsulated MnO nanocrystals for molecular and cellular MRI," was accepted in 2010 for publication in the journal "Nanoletters." Lobo earned her Bachelor of Science in biomedical engineering, with distinction, from Yale in 2010.