If $f(x)=ax+b$ is linear, why is $f(\gamma x) \neq \gamma f(x)$

Note that

$$f(x)=ax+b$$

is said to be "linear" because its graph is a straight line but (for $b\neq 0$) it is not linear in the sense of "linear map" (e.g. $f(x)=ax$).

Tags:

Linear Algebra

Linear Transformations

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