Final answer:
The horizontal asymptote of the function f(x) = (x² + 4x - 7) / (x-7) is y = 1, which is found by dividing the leading coefficients of the numerator and denominator.
Step-by-step explanation:
The horizontal asymptote of the rational function f(x) = (x² + 4x - 7) / (x-7) can be determined by considering the degrees of the polynomial in the numerator and the denominator. Since the degree of the numerator (degree 2) equals the degree of the denominator (degree 1), one must divide the leading coefficients to find the horizontal asymptote. In this case, the leading coefficient of the numerator is 1 (from x²) and the leading coefficient of the denominator is 1 (from x), resulting in a horizontal asymptote at y = 1.