Write an equation of the slant or nonlinear asymptote. $$ f(x)=\frac{x^{2}+3 x+6}{x+2} $$ The $$ \begin{array}{l}\text { (Choose one) } \nabla \text { asymptote is } y=\square \ \text { slant } \ \text { nonlinear }\end{array} $$

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1. Write the function:
   $$
   f(x)=\frac{x^{2}+3x+6}{x+2}.
   $$

2. Perform polynomial long division of $$ x^2+3x+6 $$ by $$ x+2 $$.  
   $$
   \frac{x^2+3x+6}{x+2} = x+1 + \frac{4}{x+2}.
   $$

3. The quotient $$ x+1 $$ represents the slant asymptote because as $$ x \to \pm \infty $$, the remainder term $$ \frac{4}{x+2} $$ approaches $$ 0 $$.

Thus, the slant asymptote is:
$$
y = x+1.
$$
The slant asymptote is $$ y = x + 1 $$.

Write an equation of the slant or nonlinear asymptote. \[ f(x)=\frac{x^{2}+3 x+6}{x+2} \] The \( \begin{array}{l}\text { (Choose one) } \nabla \text { asymptote is } y=\square \\ \text { slant } \\ \text { nonlinear }\end{array} \)

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