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 of x is equal to 3 x plus 1

f(x)=3x2+1
f of x is equal to 3 x squared plus 1

f(x)=6x+1
f of x is equal to 6 x plus 1

f(x)=−3x^2+1

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which function was used to create the input-output table, we can plug in the x values given in the table and see if the f(x) values match. Let's check with each function:

1. For f(x) = 3x + 1,
f(-2) = 3(-2) + 1 = -6 + 1 = -5 (not equal to -11)
f(-1) = 3(-1) + 1 = -3 + 1 = -2 (matches)
f(0) = 3(0) + 1 = 0 + 1 = 1 (matches)

2. For f(x) = 3x^2 + 1,
f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13 (not equal to -11)
f(-1) = 3(-1)^2 + 1 = 3(1) + 1 = 3 + 1 = 4 (not equal to -2)
f(0) = 3(0)^2 + 1 = 3(0) + 1 = 0 + 1 = 1 (matches)

3. For f(x) = 6x + 1,
f(-2) = 6(-2) + 1 = -12 + 1 = -11 (matches)
f(-1) = 6(-1) + 1 = -6 + 1 = -5 (not equal to -2)
f(0) = 6(0) + 1 = 0 + 1 = 1 (matches)

4. For f(x) = -3x^2 + 1,
f(-2) = -3(-2)^2 + 1 = -3(4) + 1 = -12 + 1 = -11 (matches)
f(-1) = -3(-1)^2 + 1 = -3(1) + 1 = -3 + 1 = -2 (matches)
f(0) = -3(0)^2 + 1 = -3(0) + 1 = 0 + 1 = 1 (matches)

Based on the matching values, the function that was used to create this input-output table is f(x) = -3x^2 + 1.