Consider the following three functions: G(x, y) = 4x - 9y² H(x, y, z) = 13x + y + 3z -6 I(y, z) = z - y Which of the following is true regarding the linearity of the functions? A) none of the functions is linear B) all three functions are linear C) h is linear, but g and i are not linear D) i is linear, but g and h are not linear E) h and i are linear, but g is not linear

Question

Quizplus · Accepted Answer

A function is linear if it satisfies two properties: 
1. Homogeneity: f(cx, cy) = c f(x, y)
2. Additivity: f(x1 + x2 , y1 + y2) = f(x1, y1) + f(x2, y2)

G(x, y) is not homogeneous as G(cx, cy) = 4cx - 9cy ≠ c(4x - 9y) = cG(x, y). Therefore, G(x, y) is not linear.
H(x, y, z) and I(y, z) are both homogeneous and additive. Therefore, H(x, y, z) and I(y, z) are linear.

Consider the Following Three Functions