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The core idea, one worked example, and short practice.
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A function is a machine. You put a number in, it does some arithmetic, and a number comes out. When you see , read it as “f of x.” It does not mean times .
The one move is substitution. If a question asks for , replace every in the rule with , then do the arithmetic. Exponents first, then multiply, then add or subtract.
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Two things to watch. A negative number squared turns positive, so . Absolute value bars mean distance from zero, so .
A few extra facts show up again and again: shifts the graph up units, the vertex of sits at the point , and a fraction is undefined wherever its bottom equals zero.