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)=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
f left parenthesis x right parenthesis equals 3 x squared plus 1

f(x)=6x+1

Answer 1

To determine which function corresponds to the given input-output table, we can evaluate each function at the provided values of \( x \) and compare the results with \( f(x) \) in the table.

Let's evaluate each function with the given \( x \) values:

### Function 1: \( f(x) = 3x + 1 \)

- For \( x = -2 \):
\[
f(-2) = 3(-2) + 1 = -6 + 1 = -5 \quad \text{(not } -11\text{)}
\]

### Function 2: \( f(x) = -3x^2 + 1 \)

- For \( x = -2 \):
\[
f(-2) = -3(-2)^2 + 1 = -3(4) + 1 = -12 + 1 = -11 \quad \text{(matches)}
\]

- For \( x = -1 \):
\[
f(-1) = -3(-1)^2 + 1 = -3(1) + 1 = -3 + 1 = -2 \quad \text{(matches)}
\]

- For \( x = 0 \):
\[
f(0) = -3(0)^2 + 1 = -3(0) + 1 = 0 + 1 = 1 \quad \text{(matches)}
\]

### Function 3: \( f(x) = 3x^2 + 1 \)

- For \( x = -2 \):
\[
f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13 \quad \text{(not } -11\text{)}
\]

### Function 4: \( f(x) = 6x + 1 \)

- For \( x = -2 \):
\[
f(-2) = 6(-2) + 1 = -12 + 1 = -11 \quad \text{(matches)}
\]

- For \( x = -1 \):
\[
f(-1) = 6(-1) + 1 = -6 + 1 = -5 \quad \text{(not } -2\text{)}
\]

Based on the evaluations above, only the function \( f(x) = -3x^2 + 1 \) matches all output values in the given table:

- For \( x = -2 \): \( f(-2) = -11 \)
- For \( x = -1 \): \( f(-1) = -2 \)
- For \( x = 0 \): \( f(0) = 1 \)

Thus, the correct function is:

**f(x) = -3x² + 1**