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