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 of x is equal to 6 x plus 1

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

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

f(x)=3x+1

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which of the given functions was used to create the table, we can check the values by substituting the x-values into each function.

For f(x) = 6x + 1:
- When x = -2, f(-2) = 6(-2) + 1 = -12 + 1 = -11 (matches the given value)
- When x = -1, f(-1) = 6(-1) + 1 = -6 + 1 = -5 (does not match the given value)
- When x = 0, f(0) = 6(0) + 1 = 0 + 1 = 1 (does not match the given value)

For f(x) = 3x^2 + 1:
- When x = -2, f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13 (does not match the given value)
- When x = -1, f(-1) = 3(-1)^2 + 1 = 3(1) + 1 = 3 + 1 = 4 (does not match the given value)
- When x = 0, f(0) = 3(0)^2 + 1 = 0 + 1 = 1 (matches the given value)

For f(x) = -3x^2 + 1:
- When x = -2, f(-2) = -3(-2)^2 + 1 = -3(4) + 1 = -12 + 1 = -11 (matches the given value)
- When x = -1, f(-1) = -3(-1)^2 + 1 = -3(1) + 1 = -3 + 1 = -2 (matches the given value)
- When x = 0, f(0) = -3(0)^2 + 1 = 0 + 1 = 1 (matches the given value)

For f(x) = 3x + 1:
- When x = -2, f(-2) = 3(-2) + 1 = -6 + 1 = -5 (does not match the given value)
- When x = -1, f(-1) = 3(-1) + 1 = -3 + 1 = -2 (matches the given value)
- When x = 0, f(0) = 3(0) + 1 = 0 + 1 = 1 (matches the given value)

Based on the values obtained by substituting the x-values into the functions, the function that matches all the given values in the table is f(x) = -3x^2 + 1.