# How do you find vertical, horizontal and oblique asymptotes for #(x^2 - 2x + 3) / x#?

##### 1 Answer

**Vertical asymptotes:**

Vertical asymptotes occur when the denominator of a rational function equals to 0 (this being because division by 0 is undefined in mathematics). We can find any vertical asymptotes by setting the denominator to 0 and solving.

There will be a vertical asymptote at

**Horizontal asymptotes:**

Horizontal asymptotes only occur when the degree of the denominator is higher or equal to that of the numerator. We don't have this situation in our function.

**Oblique asymptotes:**

Oblique asymptotes occur when the denominator has a lower degree than the numerator. If the function is

Therefore, we will have to divide your rational function. A thorough understanding of division of polynomials is usually a pre-requisite to finding oblique asymptotes.

The quotient is therefore

There will therefore be an oblique asymptote at

Here is the graph of the function:

Hopefully this helps!