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Functions, EXT1 F1 EQ-Bank 2 MC

Which one of the following functions in not even?

  1. \(f(x)=\sqrt{4-3x^2}\)  when  \(\abs{x} \leq \abs{\dfrac{2}{\sqrt3}}\)
  2. \(f(x)=x^2\)
  3. \(f(x)=\dfrac{1}{1+x^2}\)
  4. \(f(x)=x \sqrt{1-x^2}\)  when  \(\abs{x} \leq 1\)
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\(D\)

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\(\text{Even functions}\ \Rightarrow \ \ f(x)=f(-x) \)

\(\text{Consider option D:}\)

\(f(-x)\) \(=-x \sqrt{1-(-x)^2}\)  
  \(=-x \sqrt{1-x^2}\)  
  \(\neq f(x) \)  

 
\(\Rightarrow D\)

Functions, EXT1′ F1 2018 HSC 4 MC

Which graph best represents the curve  `y = 1/sqrt(x^2 - 4)`?
 

A.    B.   
C.    D.   
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`=>\ text(C)`

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`text(S)text(ince)\ \ sqrt(x^2 – 4) > 0`

`=> y > 0\ \ (text(Eliminate B and D))`
 

`text(As)\ x -> 2^+, sqrt(x^2 – 4) -> 0, y -> ∞`

`text(As)\ x -> -2^-, sqrt(x^2 – 4) -> 0, y -> ∞`

`=>\ text(C)`

Functions, EXT1′ F1 2012 HSC 11f

Sketch the following graphs, showing the `x`- and `y`-intercepts

  1.  `y = |\ x\ |- 1`   (1 mark)
  2.  `y = x(|\ x\ | - 1)`    (2 marks)

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  1. `text(See Worked Solutions.)`
  2. `text(See Worked Solutions.)`
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i. & ii.  

Graphs, EXT2 2012 HSC 11f Answer

`text{Note for part (ii)}`

`=>y = x(|\ x\ | – 1)\ \ text(is an ODD function)`