Use the table to answer the question.

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 3 x squared plus 1

f(x)=−3x2+1

Answer 1

To find which function corresponds to the given input-output table, we can substitute each \( x \) value into the provided functions and see if any produce the correct \( f(x) \) values.

Here are the functions to test:

1. \( f(x) = 6x + 1 \)

   • \( f(-2) = 6(-2) + 1 = -12 + 1 = -11 \) ✔️
   • \( f(-1) = 6(-1) + 1 = -6 + 1 = -5 \) (not matching) ❌
   • So, this function is not correct.

2. \( f(x) = 3x + 1 \)

   • \( f(-2) = 3(-2) + 1 = -6 + 1 = -5 \) (not matching) ❌
   • So, this function is not correct.

3. \( f(x) = 3x^2 + 1 \)

   • \( f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13 \) (not matching) ❌
   • So, this function is not correct.

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

   • \( f(-2) = -3(-2)^2 + 1 = -3(4) + 1 = -12 + 1 = -11 \) ✔️
   • \( f(-1) = -3(-1)^2 + 1 = -3(1) + 1 = -3 + 1 = -2 \) ✔️
   • \( f(0) = -3(0)^2 + 1 = 0 + 1 = 1 \) ✔️
   • This function matches all the values in the table.

The function that corresponds to the input-output table is:

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