Question

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?

Answer Options:

x = 0
x = 1
x = 2
x = -1

Answer 1

To create the input-output table for the function \( f(x) = (x + 1)^2 + 4 \), we will plug in each given value of \( x \) into the function and calculate the corresponding output \( f(x) \).

Let's calculate \( f(x) \) for each provided value of \( x \):

1. **For \( x = 0 \)**:
\[
f(0) = (0 + 1)^2 + 4 = (1)^2 + 4 = 1 + 4 = 5
\]

2. **For \( x = 1 \)**:
\[
f(1) = (1 + 1)^2 + 4 = (2)^2 + 4 = 4 + 4 = 8
\]

3. **For \( x = 2 \)**:
\[
f(2) = (2 + 1)^2 + 4 = (3)^2 + 4 = 9 + 4 = 13
\]

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

Now, let's summarize the input-output table:

| \( x \) | \( f(x) \) |
|----------|------------|
| 0 | 5 |
| 1 | 8 |
| 2 | 13 |
| -1 | 4 |

From the output values calculated:

- \( f(0) = 5 \)
- \( f(1) = 8 \)
- \( f(2) = 13 \)
- \( f(-1) = 4 \)

The largest output is 13, which occurs at \( x = 2 \).

Therefore, the value of \( x \) that produces the largest output for the function is:

**x = 2**.