QuestionDetermine the oblique asymptote for the function $f(x)=\frac{x^{2}-4}{x+2}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{x^{}-4}{x+}$ . We are looking for the equation of the oblique asymptote

STEP 2

Observe that the degree of the numerator is one more than the degree of the denominator. This means that the function has an oblique asymptote, which can be found by performing polynomial division.

STEP 3

Perform polynomial division of the numerator by the denominator.
$\frac{x^{2}-}{x+2} = x -2 + \frac{-}{x+2}$

STEP 4

The oblique asymptote is given by the quotient of the division, without the remainder.
$y = x -2$ So, the equation of the oblique asymptote of the function $f(x)=\frac{x^{2}-4}{x+2}$ is $y = x -2$ .

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