TI 89 Calculus > Horizontal Asymptotes on the TI-89

In calculus, you will be asked to find the vertical asymptotes and horizontal asymptotes of a function. The **horizontal asymptote** happens when the denominator of a rational function is zero. You don’t have to figure out horizontal asymptotes by hand: the TI-89 graphing calculator can help you find the horizontal asymptote in seconds.

## How to Find Horizontal Asymptotes on the TI-89: Steps

*Note: Make sure you are on the home screen. If you aren’t on the home screen, press the Home button.*

**Step 1:** Look at the exponents in the denominator and numerator.

If the largest exponent of the numerator is larger than the largest exponent of the denominator, there is no asymptote. That’s it! You’re Done!

If the largest exponent of the denominator of the function is larger than the largest exponent of the numerator, go to Step 2.

If the exponential degrees are the same in the numerator and denominator, go to Step 3.

**Step 2: **The horizontal asymptote will be y=0. That’s it! You’re done!

**Step 3:** Enter your function into the y=editor. For example, you might have the function f(x) = (2x^{2} – 4) / (x^{2} + 4). To enter the function into the y=editor, follow Steps 4 and 5.

**Step 4:** Press the diamond key and then F1 to enter into the y=editor.

**Step 5:** Enter the function. For example, if your function is f(x) = (2x^{2} – 4) / (x^{2} + 4) then press ( 2 x ^ 2 – 4 ) / ( x ^ 2 + 4 ) then ENTER.

**Step 6:** Press the diamond key and F5 to view a table of values for the function.

Step 7: Scroll far down the table and look the y values. You will notice that as x increases, the graph gets closer and closer and closer to y=2 but does not reach this value. The graph even hits y=1.999999. The horizontal asymptote is y=2.

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