Question

Is the function g(x)=
–
7
6
+
x
4
linear or nonlinear?

Answer 1

g(x) = -7/6 + x/4 can be written g(x) = (1/4)x - 7/6, which is a first-degree polynomial. So it is linear (slope = 1/4, y-intercept = -7/6).

(If by "linear" you mean a linear map in linear algebra sense, it's not linear because g(0) ≠ 0.)