Year 11 Maths - Methods Functions, relations and transformations

Relations, Domain And Range

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Questions

Question 1

28507

State the range of the relation \({x^2} + {y^2} = 9\)

Answer

\({\rm{Range}} = \left[ { - 3,3} \right]\)

Worked Solution

\begin{aligned}
&x^{2}+y^{2}=9 \text { is a circle with centre }\\
&(0,0) \text { and radius } 3.\\
&\text { Let } x=0 \;\; y^{2}=9 \rightarrow y=\pm 3\\
&\therefore \text { Range }=[-3,3]
\end{aligned}

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