To evaluate the function \( f(x) = 3 - 2x \), we need to understand that this function is linear, with a slope of \(-2\). This means that as \( x \) increases, the output \( f(x) \) decreases.
To find the input that generates the largest output, we should look at the function's behavior:
- When \( x \) is very small (negative), \( f(x) \) will be larger.
- As \( x \) increases, the output becomes smaller.
Thus, the largest output occurs at the smallest possible value of \( x \).
For example:
- If \( x = 0 \), then \( f(0) = 3 - 2(0) = 3 \).
- If \( x = -1 \), then \( f(-1) = 3 - 2(-1) = 3 + 2 = 5 \).
- If \( x = -2 \), then \( f(-2) = 3 - 2(-2) = 3 + 4 = 7 \).
Continuing this way, the function will keep increasing as \( x \) decreases.
Thus, the input that generates the largest output is \( x = -\infty \), theoretically. However, for practical purposes, the largest output value can be found at very high negative values of \( x \).
In conclusion, the function \( f(x) \) has larger outputs for larger negative values of \( x \).