What are the asymptotes for $\frac{x - 3}{x - 2}$ $(x-3) / (x-2)$ ?

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Answer 1 · 2015-08-08T01:52:18

There is a vertical asymptote at $x = 2$ $color(red)(x=2)$ and a horizontal asymptote at $y = 1$ $color(red)(y=1)$ .

$y = \frac{x - 3}{x - 2}$ $y=(x-3)/(x-2)$

Step 1. Find the vertical asymptotes.

Set the denominator equal to zero and solve for $x$ $x$ .

$x - 2 = 0$ $x-2=0$

$x = 2$ $x=2$

There is a vertical asymptote at $x = 2$ $x=2$ .

Step 2. Find the horizontal asymptotes.

We divide the coefficients of the highest terms.

$\frac{1}{1} = 1$ $1/1=1$

The horizontal asymptote is at $y = 1$ $y=1$ .

Graph

What are the asymptotes for (x-3) / (x-2) x−3x−2(x-3) / (x-2) ?