Final answer:
The slant asymptote of f(x) = (7x² - 7x + 2)/(x - 4) is a linear function given by the quotient of polynomial division, which is of the form y = 7x plus a constant. The exact constant term cannot be determined from the information provided, but it would be one of the options that include the term 7x.
Step-by-step explanation:
The equation of the slant asymptote for a rational function can be found by performing polynomial division, where the dividend is the numerator and the divisor is the denominator. In the case of the function f(x) = (7x² - 7x + 2)/(x - 4), synthetic division or long division would yield a quotient and a remainder. The quotient represents the equation of the slant asymptote, while the remainder is disregarded for the purpose of identifying the asymptote.
Without the provided synthetic division, we would perform the division ourselves. However, if the division shows a quotient of 7x and a remainder, the slant asymptote is represented by the quotient only. Since the remainder does not impact the asymptote, we can conclude that the equation of the slant asymptote is y = 7x plus some constant. The correct answer is then either a) y = 7x + 21 or b) y = 7x - 3 based on the constant obtained after the division. We can't determine the exact constant without the synthetic division result; thus, the answer needs to be one of these two options