1. If \( f(n)=(n-1)^{2}+3 n \), which statement is true? 1) \( f(3)=-2 \) 2) \( f(-2)=3 \) 3) \( f(-2)=-15 \) 4) \( f(-15)=-2 \)

To determine which statement is true, we will evaluate the function \( f(n) = (n-1)^2 + 3n \) for the given values of \( n \). 1. **Evaluate \( f(3) \)**: \[ f(3) = (3-1)^2 + 3 \cdot 3 = (2)^2 + 9 = 4 + 9 = 13 \] So, \( f(3) \neq -2 \). 2. **Evaluate \( f(-2) \)**: \[ f(-2) = (-2-1)^2 + 3 \cdot (-2) = (-3)^2 - 6 = 9 - 6 = 3 \] So, \( f(-2) = 3 \). 3. **Evaluate \( f(-2) \) again for confirmation**: We already calculated \( f(-2) = 3 \), so the statement \( f(-2) = -15 \) is false. 4. **Evaluate \( f(-15) \)**: \[ f(-15) = (-15-1)^2 + 3 \cdot (-15) = (-16)^2 - 45 = 256 - 45 = 211 \] So, \( f(-15) \neq -2 \). Now, summarizing the evaluations: - \( f(3) = 13 \) (not -2) - \( f(-2) = 3 \) (true) - \( f(-2) = -15 \) (false) - \( f(-15) = 211 \) (not -2) The only true statement is: \[ \boxed{2} \]