The Truncus (VCE SSCE Mathematical Methods): Flashcards

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The truncus
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Truncus definition

U-shaped curve from graphing certain reciprocal functions

Basic truncus equation

y=1x2y = \frac{1}{x^2} or y=x2y = x^{-2} for x0x \neq 0

Where basic truncus undefined

At x=0x = 0

Values produced by basic truncus

Only positive values

Vertical asymptote of y=1x2y = \frac{1}{x^2}

x=0x = 0 (the y-axis)

Horizontal asymptote of y=1x2y = \frac{1}{x^2}

y=0y = 0 (the x-axis)

General transformed truncus form

y=a(xh)2+ky = \frac{a}{(x-h)^2} + k

Vertical asymptote of y=a(xh)2+ky = \frac{a}{(x-h)^2} + k

x=hx = h

Horizontal asymptote of y=a(xh)2+ky = \frac{a}{(x-h)^2} + k

y=ky = k

Parameter 'a' in truncus transformations

Vertical stretching, compression, and reflection

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