Find the Asymptotes y=(-2(x-8))/(8-x)

$y = \frac{- 2 (x - 8)}{8 - x}$

Step 1

Find where the expression $\frac{- 2 (x - 8)}{8 - x}$ is undefined.

$x = 8$

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

Consider the rational function $R (x) = \frac{a x^{n}}{b x^{m}}$ where $n$ is the degree of the numerator and $m$ is the degree of the denominator.

1. If $n < m$ , then the x-axis, $y = 0$ , is the horizontal asymptote.

2. If $n = m$ , then the horizontal asymptote is the line $y = \frac{a}{b}$ .

3. If $n > m$ , then there is no horizontal asymptote (there is an oblique asymptote).

Step 4

Find $n$ and $m$ .

$n = 1$

$m = 1$

Step 5

Since $n = m$ , the horizontal asymptote is the line $y = \frac{a}{b}$ where $a = - 2$ and $b = - 1$ .

$y = 2$

Step 6

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

Step 7

This is the set of all asymptotes.

No Vertical Asymptotes

Horizontal Asymptotes: $y = 2$

No Oblique Asymptotes

Step 8