Problem 2-1: Linearity of Functions

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Which one(s) of the following functions is linear?

a) $y=x+1$ .
b) $y=2x+1$ .
c) $y=1$ .
d) $y=x^2+x+1$ .
e) $y=x^1+1$ .
f) $y=\frac{1}{x}$ .
g) $y=\sin(x)$ .

h) $y=\sqrt{x}$ .
i) $y=x+\frac{1}{1-x}$ .

j) $5x+2y-1=0$ .
k) $y=x+c^2$ . ( $c$ is an arbitrary constant).

Solution
a) Linear
b) Linear
c) Linear
d) Nonlinear
e) Linear
f) Nonlinear

g) Nonlinear
h) Nonlinear
i) Nonlinear
j) Linear

k) Linear

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