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Functions, 2ADV F1 2023 HSC 4 MC

The graph of a polynomial is shown.
 


  

Which row of the table is correct for this polynomial?
 

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`B`

Show Worked Solution

`text{By elimination:}`

`text{Double root where graph SP touches}\ xtext{-axis}`

`:.\ C and D\ text{incorrect}`

`(x-c)^2\ text{occurs where}\ x>0`

`:. c>0\ (A\ text{is incorrect})`

`=>B`

Functions, 2ADV F1 2021 HSC 8 MC

The graph of  `y = f(x)`  is shown.

Which of the following could be the equation of this graph?

  1. `y = (1 - x)(2 + x)^3`
  2. `y = (x + 1)(x - 2)^3`
  3. `y = (x + 1)(2 - x)^3`
  4. `y = (x - 1)(2 + x)^3`
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`C`

Show Worked Solution

`text(By elimination:)`

`text(A single negative root occurs when)\ \ x =–1`

`->\ text(Eliminate A and D)`

`text(When)\ \ x = 0, \ y > 0`

`->\ text(Eliminate B)`

`=> C`