![]() Consider the “add three” function $F(x) = x + 3$: Surprisingly, regular addition isn’t linear either. We doubled the input but quadrupled the output. Which operations are linear and predictable? Multiplication, it seems.Įxponents ($F(x) = x^2$) aren’t predictable: $10^2$ is 100, but $20^2$ is 400. In our example, $F(x)$ calculates the rise when moving forward x feet, and the properties hold:Īn operation is a calculation based on some inputs. In math terms, an operation F is linear if scaling inputs scales the output, and adding inputs adds the outputs:
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