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Functions, 2ADV F1 2025 HSC 3 MC

What is the domain of the function  \(y=\sqrt{6-x^2}\) ?

  1. \(\left(0, \sqrt{6}\right)\)
  2. \(\left[0, \sqrt{6}\right]\)
  3. \(\left(-\sqrt{6}, \sqrt{6}\right)\)
  4. \(\left[-\sqrt{6}, \sqrt{6}\right]\)
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\(D\)

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\(6-x^2 \geq 6\ \ \Rightarrow\ \ x^2 \leq 6\)

\(-\sqrt{6} \leq x \leq \sqrt{6} \)

\(\Rightarrow D\)

Functions, 2ADV F1 SM-Bank 33

  1.  State the domain and range of  `y = -sqrt(12-x^2)`.   (2 marks)

  2.  Sketch the graph.  (1 mark)

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i.  `text(Domain:)\ -sqrt12<=x<= sqrt12`

`text(Range:)\ -sqrt12<=y<= 0`

ii.   

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i.   `y = -sqrt(12-x^2)`

`text(Domain:)\ -sqrt12<=x<= sqrt12`

`text(Range:)\ -sqrt12<=y<= 0`
 

ii.