Applying Function Notation (VCE SSCE Mathematical Methods): Flashcards

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Applying Function Notation
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Function notation provides

Systematic, formal way to identify inputs and outputs

Practical domain definition

Input values that make sense in real-world context

Examples of restricted practical domains

Negative lengths, time periods, or populations

Volume of sphere formula with radius rr

V(r)=43πr3V(r) = \frac{4}{3}\pi r^3

Practical domain for sphere volume function

(0,)(0, \infty) - all positive real numbers

Linear function form

f(x)=ax+bf(x) = ax + b

Method to find parameters aa and bb in linear functions

Use two known points to form simultaneous equations

Factored form of quadratic with zeros pp and qq

f(x)=k(xp)(xq)f(x) = k(x - p)(x - q)

When to use factored form for quadratics

When you know the zeros of the function

Mathematical domain vs practical domain

Mathematical broader; practical restricted by real-world context

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