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The question is asking whether the given list of possible rational zeros is correct for the polynomial function \( f(x) = 2x^3 - 3x^2 + 4x - 6 \), based on the Rational Root Theorem.

### Applying the Rational Root Theorem:
1. **Rational Root Theorem**: It states that the possible rational zeros of a polynomial \( f(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_0 \) are given by \( \frac{q}{p} \), where:
   - \( q \) is a factor of the constant term \( a_0 \) (in this case, \( -6 \)),
   - \( p \) is a factor of the leading coefficient \( a_n \) (in this case, \( 2 \)).

2. **Constant term \( a_0 = -6 \)**: The factors of \( -6 \) are \( \pm 1, \pm 2, \pm 3, \pm 6 \).
   
3. **Leading coefficient \( a_n = 2 \)**: The factors of \( 2 \) are \( \pm 1, \pm 2 \).

4. **Possible rational zeros**: According to the Rational Root Theorem, the possible rational zeros are all combinations of \( \frac{q}{p} \), where \( q \) is a factor of \( -6 \) and \( p \) is a factor of \( 2 \). Therefore, the possible rational zeros are:
   \[
   \frac{q}{p} = \pm 1, \pm \frac{1}{2}, \pm 2, \pm 3, \pm \frac{3}{2}, \pm 6
   \]

### Comparing the provided set:
The provided set of possible rational zeros is \( \{ \pm 1, \pm 2, \pm 3, \pm 6 \} \). This set is missing \( \pm \frac{1}{2} \) and \( \pm \frac{3}{2} \), which should also be included based on the Rational Root Theorem.

### Conclusion:
The provided set of possible rational zeros is **incomplete**. Therefore, the correct answer is **No**, because the set is missing some values.

Would you like to see a more detailed breakdown or explanation? 

Here are 5 related questions you might find useful:
1. How does the Rational Root Theorem help in solving polynomial equations?
2. What are the steps to test if a rational number is a root of a polynomial?
3. How do synthetic division and the Rational Root Theorem work together in finding zeros?
4. Can irrational or complex numbers also be roots of this polynomial?
5. How would graphing this cubic function help in confirming the zeros?

**Tip:** When using the Rational Root Theorem, always include all fractions formed by the factors of the constant term and the leading coefficient.

Are the Possible Rational Zeros of f(x) = 2x^3 - 3x^2 + 4x - 6 equal to the given set q/p = {±1, ±2, ±3, ±6}?

This page provides a detailed solution to finding the possible rational zeros of the cubic polynomial f(x) = 2x^3 - 3x^2 + 4x - 6 using the Rational Root Theorem. Learn how to calculate the potential zeros by considering the factors of the constant term and leading coefficient.

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