RATIONAL FUNCTIONS Asymptotic Behavior (Page 2 of 5)

This function is undefined at x = 1.5. Let's investigate the behavior of the function near this value. Access the TABLE, then enter values of x that are slightly less than but getting closer and closer to 1.5. For example, we will use x = 1, 1.4, 1.49, 1.499 and 1.4999.

2nd TABLE key.

1 ENTER key. 1.4 ENTER key. 1.49 ENTER key. 1.499 ENTER key. 1.4999 ENTER key.

 Calculator screen image.

From the results we observe that as x approaches the value 1.5 from the left, the function values get increasingly large in the negative direction. We say that y approaches negative infinity, or that y decreases without bound.
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