Question

Use the table to answer the question.

x f(x)

−2
−11

−1
−2

0 1
Determine which of the given functions was used to create this input-output table.

(1 point)
Responses

f(x)=6x+1
f left parenthesis x right parenthesis equals 6 x plus 1

f(x)=3x+1
f left parenthesis x right parenthesis equals 3 x plus 1

f(x)=−3x2+1
f left parenthesis x right parenthesis equals negative 3 x squared plus 1

f(x)=3x2+1

Answer 1

To determine which function corresponds to the provided input-output table, we can evaluate each function option using the given x values and check if they produce the correct f(x) outputs.

**Given table data:**
- When \( x = -2 \), \( f(x) = -11 \)
- When \( x = -1 \), \( f(x) = -2 \)
- When \( x = 0 \), \( f(x) = 1 \)

Let's evaluate each function:

1. **Evaluate \( f(x) = 6x + 1 \)**:
- When \( x = -2 \):
\[
f(-2) = 6(-2) + 1 = -12 + 1 = -11 \quad \text{(correct)}
\]
- When \( x = -1 \):
\[
f(-1) = 6(-1) + 1 = -6 + 1 = -5 \quad \text{(not correct)}
\]

2. **Evaluate \( f(x) = 3x + 1 \)**:
- When \( x = -2 \):
\[
f(-2) = 3(-2) + 1 = -6 + 1 = -5 \quad \text{(not correct)}
\]

3. **Evaluate \( f(x) = -3x^2 + 1 \)**:
- When \( x = -2 \):
\[
f(-2) = -3(-2)^2 + 1 = -3(4) + 1 = -12 + 1 = -11 \quad \text{(correct)}
\]
- When \( x = -1 \):
\[
f(-1) = -3(-1)^2 + 1 = -3(1) + 1 = -3 + 1 = -2 \quad \text{(correct)}
\]
- When \( x = 0 \):
\[
f(0) = -3(0)^2 + 1 = 0 + 1 = 1 \quad \text{(correct)}
\]

4. **Evaluate \( f(x) = 3x^2 + 1 \)**:
- When \( x = -2 \):
\[
f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13 \quad \text{(not correct)}
\]

Based on the evaluations, the function that matches all given outputs from the table is:

**f(x) = -3x^2 + 1**.