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Functions, MET2 2022 VCAA 15 MC

The maximal domain of the function with rule `f(x)=\sqrt{x^2-2 x-3}` is given by

  1. `(-\infty, \infty)`
  2. `(-\infty,-3) \cup(1, \infty)`
  3. `(-1,3)`
  4. `[-3,1]`
  5. `(-\infty,-1] \cup[3, \infty)`
Show Answers Only

`E`

Show Worked Solution

`f(x)=\sqrt{x^2-2 x-3}`

`:. \ x^2-2 x-3 >= 0`

`:. \ (x  –  3)(x + 1)>=0`
  

So, `x <= -1` and `x >= 3`

`=>E`

 

Graphs, MET2 2008 VCAA 22 MC

The graph of the function  `f` with domain  `[0, 6]`  is shown below.

VCAA 2008 22mc

Which one of the following is not true?

  1. The function is not continuous at  `x = 2`  and  `x = 4.`
  2. The function exists for all values of `x` between `0` and `6.`
  3. `f(x) = 0`  for  `x = 2`  and  `x = 5.`
  4.  The function is positive for  `x ∈ [0, 5).`
  5. The gradient of the function is not defined at  `x = 4.`
Show Answers Only

`C`

Show Worked Solution

`f(x) > 0\ \ text(for)\ \ x = 2`

`:.\ text(Option)\ \  C\ \ text(is not true)`

`=>   C`