Determine the oblique asymptote of the graph of the function. $$ g(x)=\frac{x^{2}+4 x-4}{x+2} $$

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Given the function
$$
g(x)=\frac{x^2+4x-4}{x+2},
$$
we perform polynomial long division to find the oblique asymptote.

1. Divide $$x^2$$ (the first term of the numerator) by $$x$$ (the first term of the denominator) to obtain $$x$$.

2. Multiply the divisor by $$x$$:
   $$
   x(x+2)=x^2+2x.
   $$

3. Subtract this from the numerator:
   $$
   (x^2+4x-4)-(x^2+2x)=2x-4.
   $$

4. Divide $$2x$$ by $$x$$ to get $$2$$.

5. Multiply the divisor by $$2$$:
   $$
   2(x+2)=2x+4.
   $$

6. Subtract again:
   $$
   (2x-4)-(2x+4)=-8.
   $$

The division gives:
$$
g(x)=x+2+\frac{-8}{x+2}.
$$
Since the remainder term $$\frac{-8}{x+2}$$ approaches $$0$$ as $$x\to\pm\infty$$, the oblique asymptote is given by the quotient:
$$
y=x+2.
$$
The oblique asymptote of the function $$ g(x) = \frac{x^2 + 4x - 4}{x + 2} $$ is $$ y = x + 2 $$.

Determine the oblique asymptote of the graph of the function.

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