Answer
(a) We can see the completed tables for the function below.
(b) $y \to -\infty$ as $x \to 2^{-}$
$y \to \infty$ as $x \to 2^{+}$
(c) $y \to 1$ as $x \to \infty$
$y \to 1$ as $x \to -\infty$
Work Step by Step
(a) $r(x) = \frac{x}{x-2}$
We can see the completed tables for the function below.
(b) With the information in Table 1:
$y \to -\infty$ as $x \to 2^{-}$
With the information in Table 2:
$y \to \infty$ as $x \to 2^{+}$
(c) With the information in Table 3:
$y \to 1$ as $x \to \infty$
With the information in Table 4:
$y \to 1$ as $x \to -\infty$