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I think there's a lot of variation in content of precalculus. I had a semester of theory of functions and semester of analytic geometry, both including some aspects of calculus itself, in a strong public school. But in some ways you could have skipped that stuff and moved right into calculus after algebra two trig. Rotations were definitely included. And ...


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I'll give a less elegant answer: because the dilations and translations are easy to understand and implement. If we were interested in preserving shape under the transformations then surely rigid motions or orthogonal transformations would be a better scope for the discussion. Sadly, highschool students (in the USA) do not typically learn linear algebra, ...


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We can think of these transformations from two perspectives: as mappings of the plane or as graphs of pre/post composition of the function. For instance, the map $T: \mathbb{R}^2 \to \mathbb{R}^2$ given by $(a,b) \mapsto (a+2,b)$ is the translation of the plane two units to the right. Let $\phi: \mathbb{R} \to \mathbb{R}$ be the function $\phi(x) = x-2$. ...


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