Porisma
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What can go in, and what can come out?

What can go in, and what can come out? · Diagrams · Complete reading

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Four representations of a relation

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Source y=x+2 shown as table 0→2,1→3,2→4,3→5, corresponding set arrows, equation and full line with intercepts −2 and 2. Functions form a subset of relations.
Source y=x+2 shown as table 0→2,1→3,2→4,3→5, corresponding set arrows, equation and full line with intercepts −2 and 2. Functions form a subset of relations.
Source y=x+2 shown as table 0→2,1→3,2→4,3→5, corresponding set arrows, equation and full line with intercepts −2 and 2. Functions form a subset of relations.
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One output per input, and the square mapping

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Source valid mapping 0→2,1→3,2→4,3→5 versus invalid relation with an additional 0→3 arrow. Square mapping 1→1,2→4,3→9,4→16 has domain{1,2,3,4}, range{1,4,9,16}. Function machine takes x to f(x).
Source valid mapping 0→2,1→3,2→4,3→5 versus invalid relation with an additional 0→3 arrow. Square mapping 1→1,2→4,3→9,4→16 has domain{1,2,3,4}, range{1,4,9,16}. Function machine takes x to f(x).
Source valid mapping 0→2,1→3,2→4,3→5 versus invalid relation with an additional 0→3 arrow. Square mapping 1→1,2→4,3→9,4→16 has domain{1,2,3,4}, range{1,4,9,16}. Function machine takes x to f(x).
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Even and odd source curves

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Cosine and x² reflect in the y-axis; sine and x³ have half-turn symmetry about the origin. Horizontal axis x and vertical axis y correct stray source axis labels.
Cosine and x² reflect in the y-axis; sine and x³ have half-turn symmetry about the origin. Horizontal axis x and vertical axis y correct stray source axis labels.
Cosine and x² reflect in the y-axis; sine and x³ have half-turn symmetry about the origin. Horizontal axis x and vertical axis y correct stray source axis labels.
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Modulus selects one of two rules

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V-shaped y=absolute x consists of y=−x for x<0 and y=x for x≥0, joined at included origin.
V-shaped y=absolute x consists of y=−x for x<0 and y=x for x≥0, joined at included origin.
V-shaped y=absolute x consists of y=−x for x<0 and y=x for x≥0, joined at included origin.
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Cosine repeats after two pi

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Cosine from −4π to 4π with four adjacent peak-to-peak intervals each labelled 2π.
Cosine from −4π to 4π with four adjacent peak-to-peak intervals each labelled 2π.
Cosine from −4π to 4π with four adjacent peak-to-peak intervals each labelled 2π.
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