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The problem involves analyzing the function \( f(x) = \frac{2x+1}{x-1} \).

1. **Type of Function**: First, let's determine whether \( f(x) \) is even, odd, or neither.
   - A function is even if \( f(-x) = f(x) \).
   - A function is odd if \( f(-x) = -f(x) \).
   - If neither condition is met, the function is neither even nor odd.

2. **Asymptotes**: Next, we'll look for any vertical or horizontal asymptotes.
   - A vertical asymptote occurs where the denominator is zero, unless the same factor also zeros out the numerator.
   - A horizontal asymptote is determined by the degrees of the numerator and denominator or the behavior of \( f(x) \) as \( x \) approaches infinity or negative infinity.

3. **Graphing**: Finally, we'll sketch the graph based on this analysis.

Let's start by identifying if \( f(x) \) is even, odd, or neither:

For even:
\[ f(-x) = \frac{2(-x) + 1}{-x - 1} = \frac{-2x + 1}{-x - 1} \]
\[ f(-x) \neq f(x) \]

For odd:
\[ f(-x) = \frac{-2x + 1}{-x - 1} = \frac{2x - 1}{x + 1} \]
\[ f(-x) \neq -f(x) \]

Thus, \( f(x) \) is neither even nor odd.

For the asymptotes:
- **Vertical asymptote**: Set \( x - 1 = 0 \), so \( x = 1 \).
- **Horizontal asymptote**: Since the degrees of the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients: \( y = \frac{2}{1} = 2 \).

Let's graph this function to visualize it better.

Diberikan fungsi f(x) = (2x + 1) / (x - 1). Apakah fungsi tersebut merupakan fungsi genap, ganjil, atau bukan keduanya? Kemudian sketsakan grafiknya!

Explore whether the rational function f(x) = (2x + 1) / (x - 1) is even, odd, or neither, and learn how to sketch its graph. The problem involves understanding function symmetry and finding vertical and horizontal asymptotes. Suitable for high school students (Grades 10-12).

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