Final answer:
To determine the function rule, we test each option with the given inputs and outputs, and find that the correct answer is to multiply the input by -2. This function rule correctly translates all the given inputs to their respective outputs.
Step-by-step explanation:
The question involves determining the function rule for a function machine based on given inputs and outputs. We are given that an input of 3 produces an output of -6, an input of -2 produces an output of 4, and an input of 0 produces an output of 0. Let's test the provided options:
- Multiply the input by -2: If we use this rule, input 3 gives us 3 × -2 = -6 (which matches), and input -2 gives us -2 × -2 = +4 (which also matches).
- Multiply the input by -1 and then add 2: Input 3 gives us (3 × -1) + 2 = -1 + 2 = 1 (which does not match).
- Multiply the input by 2: Input 3 gives us 3 × 2 = 6 (which does not match).
- Multiply the input by -1 and then subtract 3: Input 3 gives us (3 × -1) - 3 = -3 - 3 = -6 (which matches), but input -2 gives us (-2 × -1) - 3 = 2 - 3 = -1 (which does not match).
Through this process of elimination, the correct answer is to multiply the input by -2. This function rule works for all the given inputs and outputs.