Final answer:
The error in listing the possible rational zeros of the function f(x) is the omission of ±1 and ±9/2, as all factors of the constant term should be considered potential zeros according to the Rational Zero Theorem.
Step-by-step explanation:
The student is trying to list the possible rational zeros of the polynomial function f(x) = x³ + 3x² - 8x - 18 using the Rational Zero Theorem. The theorem states that any rational zero, expressed in lowest terms p/q, must have p as a factor of the constant term (in this case, -18) and q as a factor of the leading coefficient (here, 1). Therefore, the possible rational zeros of f(x) are the factors of -18, which include ±2, ±3, ±6, ±9, and also ±1 and ±9/2. The error in the student's list is the omission of ±1 and ±9/2.