Classify a relation and state its domain and range practice questions | Mathematical Methods (Year 11, VCE Units 1 & 2, Functions and relations, Function notation and relations)

(a)2 marks

Read the relation and state its domain and range

D=\left\{-6,\;-2,\;2\right\},\qquad R=\left\{-3,\;2,\;3\right\}

D=\left\{-6,\;-2,\;2\right\},\qquad R=\left\{-5,\;-3,\;2,\;3\right\}

D=\left\{-6,\;-2,\;2,\;2\right\},\qquad R=\left\{-5,\;-3,\;2,\;3\right\}

D=\left\{-5,\;-3,\;2,\;3\right\},\qquad R=\left\{-6,\;-2,\;2\right\}

(b)2 marks

Determine the function status and choose its supporting explanation

The relation is a function because no input is paired with two different outputs

The relation is a function because every output is paired with at most one input

The relation is a function because no horizontal line meets the relation more than once

The relation is not a function because at p=2 it has the two outputs -3 and 3

(c)1 mark

Classify how inputs are paired with outputs

many-to-many: inputs and outputs are both repeated

one-to-many: one input has more than one output

one-to-one: no input or output is repeated

many-to-one: different inputs share an output