To evaluate the function \( f(x) = 3 - 2x \), we need to determine how the output changes based on different inputs \( x \).
The function \( f(x) \) decreases as \( x \) increases because the coefficient of \( x \) is negative (-2). This means that as \( x \) becomes larger, \( f(x) \) becomes smaller.
To find the largest output, we can consider the behavior of the function:
-
When \( x = 0 \): \[ f(0) = 3 - 2(0) = 3 \]
-
When \( x = 1 \): \[ f(1) = 3 - 2(1) = 3 - 2 = 1 \]
-
When \( x = 2 \): \[ f(2) = 3 - 2(2) = 3 - 4 = -1 \]
-
When \( x = -1 \): \[ f(-1) = 3 - 2(-1) = 3 + 2 = 5 \]
-
When \( x = -2 \): \[ f(-2) = 3 - 2(-2) = 3 + 4 = 7 \]
As observed, the function continues to increase as \( x \) decreases. Consequently, there is no upper bound since for very large negative values of \( x \), \( f(x) \) can become arbitrarily large.
Therefore, the input that generates the largest output in this function is not limited to positive integers or any fixed set of inputs; instead, the function's output increases indefinitely as \( x \) approaches negative infinity.
Thus, we conclude: The largest output for \( f(x) = 3 - 2x \) occurs as \( x \) approaches negative infinity (\( x \to -\infty \)).