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: Scaling the inputs scales the output proportionally.
2) Additivity: The function of the sum of two inputs is equal to the sum of the function of the individual inputs.

g(x, y) = 4x - 9y is not linear because it fails the homogeneity property (scaling the inputs results in a non-proportional scaling of the output).
h(x, y, z) =13x+ y + 3z - 6 satisfies both properties and therefore is linear.
i(y, z) = z - y satisfies both properties and is also linear.

Therefore, the correct answer is E, h and i are linear, but g is not linear.

Consider the Following Three Functions