Identify all asymptotes 12. $$ f(x)=\frac{2 x+3}{x-5} $$

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1. **Vertical Asymptote:**

The vertical asymptote occurs where the denominator is zero (and the numerator is not zero). For 
   $$
   f(x)=\frac{2x+3}{x-5},
   $$
   set the denominator equal to zero:
   $$
   x-5=0 \quad \Rightarrow \quad x=5.
   $$
   Thus, the vertical asymptote is $$ x=5 $$.

2. **Horizontal Asymptote:**

Since the degrees of the numerator and denominator are both 1, the horizontal asymptote is determined by the ratio of the leading coefficients. The numerator has a leading coefficient of 2, and the denominator has a leading coefficient of 1. Therefore:
   $$
   y=\frac{2}{1}=2.
   $$
   So, the horizontal asymptote is $$ y=2 $$.

The asymptotes for $$ f(x)=\frac{2x+3}{x-5} $$ are:
- Vertical asymptote: $$ x=5 $$
- Horizontal asymptote: $$ y=2 $$
The function $$ f(x)=\frac{2x+3}{x-5} $$ has a vertical asymptote at $$ x=5 $$ and a horizontal asymptote at $$ y=2 $$.

Identify all asymptotes
12.

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