Representing Functions Quick Check

Question

1 of 51 of 5 Items
Question
Use the table to answer the question.

x f(x)
𝑓
(
𝑥
)
−1
−
1

0
1
2
Finish creating the input-output table for the function f(x)=−(x+1)2+4
𝑓
(
𝑥
)
=
−
(
𝑥
+
1
)
2
+
4
. Which of the given x values produces the largest output for the function?

(1 point)
Responses

x=−1
𝑥
=
−
1
x equals negative 1

x=0
𝑥
=
0
x equals 0

x=2
𝑥
=
2
x equals 2

x=1

Answer 1

To find which of the given x values produces the largest output for the function \( f(x) = -(x + 1)^2 + 4 \), we need to evaluate the function at each of the provided x values.

Calculation:

1. For \( x = -1 \): \[ f(-1) = -((-1) + 1)^2 + 4 = -(0)^2 + 4 = 0 + 4 = 4 \]

2. For \( x = 0 \): \[ f(0) = -(0 + 1)^2 + 4 = -1^2 + 4 = -1 + 4 = 3 \]

3. For \( x = 1 \): \[ f(1) = -(1 + 1)^2 + 4 = -2^2 + 4 = -4 + 4 = 0 \]

4. For \( x = 2 \): \[ f(2) = -(2 + 1)^2 + 4 = -3^2 + 4 = -9 + 4 = -5 \]

Summary of Outputs:

• \( f(-1) = 4 \)
• \( f(0) = 3 \)
• \( f(1) = 0 \)
• \( f(2) = -5 \)

Conclusion:

The largest output occurs when \( x = -1 \).

So the answer is: x = -1