Use the table to answer the question.

Question

x f(x)
−1
0
1
2
Finish creating the input-output table for the function 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 equals negative 1

x=0
x equals 0

x=2
x equals 2

x=1
x equals 1

Answer 1

To complete the input-output table for the function $f(x)=-(x+1{)}^2+4$, we will calculate the output for each given $x$.

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 $x=2$: $$f(2)=-(2+1{)}^2+4=-3^2+4=-9+4=-5$$

Now, let's summarize the results in the table:

| x | f(x) | |----|------| | -1 | 4 | | 0 | 3 | | 1 | 0 | | 2 | -5 |

Now we can see the outputs:

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

The largest output from the calculated values is $4$, which corresponds to $x=-1$.

Therefore, the value of $x$ that produces the largest output for the function is:

x = -1