Data Transformations (VCE SSCE General Mathematics): Flashcards

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Data Transformations
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Data transformation definition

Changing a variable's scale using a mathematical function

Linearisation meaning

Transforming data to make a non-linear relationship linear

Two main transformations in this topic

Squared (x2x^2) and reciprocal (1x\frac{1}{x})

Squared transformation (x2x^2): axis change

Horizontal axis changes from xx to x2x^2

When to use squared transformation (x2x^2)

For parabolic relationships where yx2y \propto x^2

Reciprocal transformation (1x\frac{1}{x}): axis change

Horizontal axis changes from xx to 1x\frac{1}{x}

When to use reciprocal transformation (1x\frac{1}{x})

For hyperbolic/inverse variation where y1xy \propto \frac{1}{x}

Direct variation characteristic

As xx increases, yy increases

Inverse variation characteristic

As xx increases, yy decreases

Slope of linearised graph represents

The constant of variation (kk)

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