Use the table to answer the question.

To determine which function corresponds to the provided input-output table, we can evaluate each function option using the given x values and check if they produce the correct f(x) outputs.

Given table data:

• When \( x = -2 \), \( f(x) = -11 \)
• When \( x = -1 \), \( f(x) = -2 \)
• When \( x = 0 \), \( f(x) = 1 \)

Let's evaluate each function:

1. Evaluate \( f(x) = 6x + 1 \):

   • When \( x = -2 \): \[ f(-2) = 6(-2) + 1 = -12 + 1 = -11 \quad \text{(correct)} \]
   • When \( x = -1 \): \[ f(-1) = 6(-1) + 1 = -6 + 1 = -5 \quad \text{(not correct)} \]

2. Evaluate \( f(x) = 3x + 1 \):

   • When \( x = -2 \): \[ f(-2) = 3(-2) + 1 = -6 + 1 = -5 \quad \text{(not correct)} \]

3. Evaluate \( f(x) = -3x^2 + 1 \):

   • When \( x = -2 \): \[ f(-2) = -3(-2)^2 + 1 = -3(4) + 1 = -12 + 1 = -11 \quad \text{(correct)} \]
   • When \( x = -1 \): \[ f(-1) = -3(-1)^2 + 1 = -3(1) + 1 = -3 + 1 = -2 \quad \text{(correct)} \]
   • When \( x = 0 \): \[ f(0) = -3(0)^2 + 1 = 0 + 1 = 1 \quad \text{(correct)} \]

4. Evaluate \( f(x) = 3x^2 + 1 \):

   • When \( x = -2 \): \[ f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13 \quad \text{(not correct)} \]

Based on the evaluations, the function that matches all given outputs from the table is:

f(x) = -3x^2 + 1.