Question

f of X = -x + 1 to the second + 4 which of the given X values produces the largest output for the functions negative 1, 1, 0 or 2

Answer 1

To find which \( x \) value produces the largest output for the function \( f(x) = -(x^2) + 4 \), we'll calculate \( f(x) \) for each given \( x \) value: -1, 1, 0, and 2.

1. **For \( x = -1 \)**:
\[
f(-1) = -((-1)^2) + 4 = -1 + 4 = 3
\]

2. **For \( x = 1 \)**:
\[
f(1) = -(1^2) + 4 = -1 + 4 = 3
\]

3. **For \( x = 0 \)**:
\[
f(0) = -(0^2) + 4 = -0 + 4 = 4
\]

4. **For \( x = 2 \)**:
\[
f(2) = -(2^2) + 4 = -4 + 4 = 0
\]

Now, let's summarize the outputs:
- \( f(-1) = 3 \)
- \( f(1) = 3 \)
- \( f(0) = 4 \)
- \( f(2) = 0 \)

The largest output is \( 4 \), which occurs at \( x = 0 \).

Thus, the \( x \) value that produces the largest output is \( \boxed{0} \).