The function \( f(x) = \frac{2x - 1}{x + 4} \) has a horizontal asymptote at what value?

["Understanding the Horizontal Asymptote of ( f(x) = \frac{2x - 1}{x + 4} )", "When analyzing rational functions like ( f(x) = \frac{2x - 1}{x + 4} ), one of the most important features to identify is the horizontal asymptote. This line tells us the behavior of the function as ( x ) approaches positive or negative infinity. For rational functions, where both the numerator and denominator are polynomials, horizontal asymptotes depend on the degrees of these polynomials.", "### Step 1: Determine the degrees of numerator and denominator\nIn ( f(x) = \frac{2x - 1}{x + 4} ):\n- The degree of the numerator ( 2x - 1 ) is 1.\n- The degree of the denominator ( x + 4 ) is also 1.", "### Step 2: Use the rule for horizontal asymptotes based on degree comparison\n- If the degree of the numerator equals the degree of the denominator, the horizontal asymptote occurs at the ratio of the leading coefficients.", "Here, both polynomials are degree 1:\n- Leading term of numerator: ( 2x ) → coefficient = 2\n- Leading term of denominator: ( x ) → coefficient = 1", "Thus, the horizontal asymptote is:\n[\ny = \frac{2}{1} = 2\n]", "### Conclusion\nThe function ( f(x) = \frac{2x - 1}{x + 4} ) has a horizontal asymptote at ( y = 2 ). This means as ( x ) becomes very large or very negative, the value of ( f(x) ) approaches 2 but never actually reaches it.", "Understanding horizontal asymptotes helps in graphing rational functions and predicting long-term behavior—key concepts in algebra and calculus.", "---", "Key Takeaway:\nThe horizontal asymptote of ( f(x) = \frac{2x - 1}{x + 4} ) is ( y = 2 ). This value arises directly from the ratio of leading coefficients since the degrees are equal."]