To determine the horizontal asymptote of the function f(x) = (7x + 1) / (2x – 9), we need to analyze the degrees of the polynomial in the numerator and the polynomial in the denominator.
1. **Identify the Degrees**: Both the numerator and the denominator are linear polynomials, meaning their highest degree is 1.
2. **Compare the Leading Coefficients**: Since the degrees are the same (both 1), the horizontal asymptote is found by taking the ratio of the leading coefficients. In this case, the leading coefficient of the numerator (7) and the leading coefficient of the denominator (2) gives us:
Horizontal Asymptote: y = 7/2
Thus, the horizontal asymptote of the function f(x) = (7x + 1) / (2x – 9) is y = 3.5.