is f(x) = ax+b a linear function?


Is f(x) = ax + b (where b, a <> 0) a linear function?

Everyone calls this linear but check this out:

f(y) = ay + b
f(z) = az + b

f(y+z) = a(y+z) + b = ay+ az + b <> f(y) + f(z) = ay+ az + 2b

f(cy) = a(cy) + b = cay + b <> cf(c) = cay + cb


f(x) fails both conditions for linearity. So why is it called linear
function?

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