Question

F(x) = {

9 - 3x if x < 1
3x^2 - 6x + 6 if 1 ≤ x < 3
DNE (Does Not Exist) if x ≥ 3
}

Answer 1

Option a, y = 13x, corresponds to the given conditions for the function f(x) = {9 - 3x if x < 1, 13x^2 - 6x + 6 if 1 ≤ x < 3, DNE if x ≥ 3}.

Step-by-step explanation:

The given function f(x) is defined piecewise with two cases:

1. If x < 1, then f(x) = 9 - 3x
2. If 1 ≤ x < 3, then f(x) = 13x^2 - 6x + 6
3. If x ≥ 3, then f(x) does not exist (DNE)

To determine which option corresponds to the given conditions, we need to analyze the slope and behavior of the options. Option b, y = x², corresponds to a positive slope that is increasing with x, so it does not match the given conditions. Option a, y = 13x, corresponds to a positive slope that is decreasing with x, which matches the given conditions. Therefore, option a corresponds to f(x).