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)=3x2+1
f left parenthesis x right parenthesis equals 3 x squared 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)=6x+1

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To determine which function was used to create the input-output table, we can evaluate each given function at one or more of the x-values from the table and check whether the function yields the corresponding f(x) from the table.

Let's evaluate each function for x = -2 (since this is a unique value that should help us eliminate incorrect functions):

1. f(x) = 3x^2 + 1
f(-2) = 3(-2)^2 + 1
f(-2) = 3(4) + 1
f(-2) = 12 + 1
f(-2) = 13
This does not match the table (f(-2) = -11).

2. f(x) = 3x + 1
f(-2) = 3(-2) + 1
f(-2) = -6 + 1
f(-2) = -5
This does not match the table (f(-2) = -11).

3. f(x) = −3x^2 + 1
f(-2) = −3(-2)^2 + 1
f(-2) = −3(4) + 1
f(-2) = −12 + 1
f(-2) = -11
This matches the table (f(-2) = -11).

4. f(x) = 6x + 1
f(-2) = 6(-2) + 1
f(-2) = -12 + 1
f(-2) = -11
Although this matches the value at x = -2, we need to check other values to ensure this is not a coincidence.

To confirm our selection, let's evaluate the third function (f(x) = −3x^2 + 1) at x = -1 and x = 0 (both provided in the table):

For x = -1:
f(x) = −3x^2 + 1
f(-1) = −3(-1)^2 + 1
f(-1) = −3(1) + 1
f(-1) = −3 + 1
f(-1) = -2
This matches the table (f(-1) = -2).

For x = 0:
f(x) = −3x^2 + 1
f(0) = −3(0)^2 + 1
f(0) = −3(0) + 1
f(0) = 0 + 1
f(0) = 1
This matches the table (f(0) = 1).

Given that f(x) = −3x^2 + 1 matches all provided values in the table, we can conclude that the correct function is:

f(x) = −3x^2 + 1