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Functions and Graphs, SMB-019

Shade the region defined by  `y+3x>3`  on the graph below and verify your result.  (3 marks)

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`text{Test}\ (0,0):`

`3(0)-4(0)<12\ \ =>\ \ 0<12\ \ text{(Incorrect – not in shaded area)}`

Show Worked Solution

`xtext{-intercept occurs when}\ y=0:`

`0+3x=3\ \ =>\ \ x=1`

`ytext{-intercept occurs when}\ x=0:`

`y+3(0)=3\ \ =>\ \ y=3`

`text{Test}\ (0,0):`

`0+3(0)>3\ \ =>\ \ 0>3\ \ text{(Incorrect – not in shaded area)}`

Functions and Graphs, SMB-018

Shade the region defined by  `x/2-y>0`  on the graph below and verify your result.  (2 marks)

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`text{Test}\ (1,0):`

`1/2-0>0\ \ text{(correct)}`

Show Worked Solution

`xtext{-intercept occurs when}\ y=0:`

`x/2-0=0\ \ =>\ \ x=0`

`text{Graph cuts at}\ (0,0)`

`text{Also passes through}\ (2,1)`
 

`text{Test}\ (1,0):`

`1/2-0>0\ \ text{(Correct – in shaded area)}`

Functions and Graphs, SMB-017

  1. Express the function  `5y-3x=15`  in the form  `y=mx+b`.  (1 mark)

  2. Shade the region defined by  `5y-3x>15`  on the graph below and verify your result.  (3 marks)
      

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i.    `y=3/5x+3`

ii.  

`text{Test}\ (0,0):`

`5(0)-3(0)>15\ \ =>\ \ 0<15\ \ text{(incorrect)}`

Show Worked Solution
i.     `5y-3x` `=15`
  `5y` `=3x+15`
  `y` `=3/5x+3`

 

ii.   `xtext{-intercept occurs when}\ y=0:`

`5(0)-3x=15\ \ =>\ \ x=-5`

`ytext{-intercept at}\ \ y=3`

`text{Test}\ (0,0):`

`5(0)-3(0)>15\ \ =>\ \ 0>15\ \ text{(Incorrect – not in shaded area.)}`

Functions and Graphs, SMB-016

Shade the region defined by  `3x-4y<12`  on the graph below and verify your result.  (3 marks)
 


Show Answers Only

`text{Test}\ (0,0):`

`3(0)-4(0)<12\ \ =>\ \ 0<12\ \ text{(correct)}`

Show Worked Solution

`xtext{-intercept occurs when}\ y=0:`

`3x-4(0)=12\ \ =>\ \ x=4`

`ytext{-intercept occurs when}\ x=0:`

`3(0)-4y=12\ \ =>\ \ y=-3`

`text{Test}\ (0,0):`

`3(0)-4(0)<12\ \ =>\ \ 0<12\ \ text{(Correct – is in shaded area)}`

Functions, EXT1* F1 2017 HSC 8 MC

The region enclosed by  `y = 4 - x,\ \ y = x`  and  `y = 2x + 1`  is shaded in the diagram below.
 

Which of the following defines the shaded region?

A.   `y <= 2x + 1, qquad` `y <= 4-x, qquad` `y >= x`
B.   `y >= 2x + 1, qquad` `y <= 4-x, qquad` `y >= x`
C.   `y <= 2x + 1, qquad` `y >= 4-x, qquad` `y >= x`
D.   `y >= 2x + 1, qquad` `y >= 4-x, qquad` `y >= x`
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`A`

Show Worked Solution

`text(Consider)\ \ y = 2x + 1,`

`text(Shading is below graph)`

`=> y <= 2x + 1`

`text(Consider)\ \ y = 4-x,`

`text(Shading is below graph)`

`=> y <= 4-x`

`=>  A`