Question
Evaluate the function for following input: f(x) = 3 - 2x. Which input generates the largest output when evaluating the function?
Answers
GPT-4o mini
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:
1. When \( x = 0 \):
\[
f(0) = 3 - 2(0) = 3
\]
2. When \( x = 1 \):
\[
f(1) = 3 - 2(1) = 3 - 2 = 1
\]
3. When \( x = 2 \):
\[
f(2) = 3 - 2(2) = 3 - 4 = -1
\]
4. When \( x = -1 \):
\[
f(-1) = 3 - 2(-1) = 3 + 2 = 5
\]
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 (\( x \to -\infty \)).
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:
1. When \( x = 0 \):
\[
f(0) = 3 - 2(0) = 3
\]
2. When \( x = 1 \):
\[
f(1) = 3 - 2(1) = 3 - 2 = 1
\]
3. When \( x = 2 \):
\[
f(2) = 3 - 2(2) = 3 - 4 = -1
\]
4. When \( x = -1 \):
\[
f(-1) = 3 - 2(-1) = 3 + 2 = 5
\]
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 (\( x \to -\infty \)).