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Functions, 2ADV F1 2020 HSC 1 MC

Which inequality gives the domain of  `y = sqrt(2x-3)`?

  1. `x < 3/2`
  2. `x > 3/2`
  3. `x <= 3/2`
  4. `x >= 3/2`
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`D`

Show Worked Solution

`text(Domain exists when:)`

`2x-3` `>= 0`
`2x` `>= 3`
`x` `>= 3/2`

  
`=>D`

Filed Under: Functions and Other Graphs, Further Functions and Relations (Y11), Other Functions and Relations (Adv-2027) Tagged With: Band 4, num-title-ct-patha, num-title-qs-hsc, smc-4244-10-Domain, smc-4244-70-Square root, smc-6218-40-Square-Root Functions, smc-987-20-Inequalities, smc-987-40-Square-Root Functions

Functions, 2ADV F1 2019 HSC 2 MC

What values of  `x`  satisfy  `4-3x <= 12`?

  1. `x <= -16/3`
  2. `x >= -16/3`
  3. `x <= -8/3`
  4. `x >= -8/3`
Show Answers Only

`D`

Show Worked Solution
`4-3x` `<= 12`
`-3x` `<= 8`
`x` `>= -8/3` 

 
`=>  D`

Filed Under: Further Functions and Relations (Y11), Inequalities, Linear Functions (Adv-2027) Tagged With: Band 3, num-title-ct-pathb, num-title-qs-hsc, smc-4385-10-Linear, smc-6214-08-Inequalities, smc-987-20-Inequalities

Functions, 2ADV F1 2018 HSC 11b

Solve  `1 - 3x > 10`.  (2 marks)

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`x < -3`

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`1 – 3x` `> 10`
`-3x` `> 9`
`x` `< -3`

Filed Under: Further Functions and Relations (Y11), Inequalities and Absolute Values, Linear Functions (Adv-2027) Tagged With: Band 3, smc-6214-08-Inequalities, smc-987-20-Inequalities

Functions, 2ADV F1 2007 HSC 1b

Solve  `2x-5> -3`  and graph the solution on a number line.  (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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`x > 1`
 

Show Worked Solution
`2x-5` `> -3`
`2x` `> 2`
`x` `> 1`

 

Filed Under: Further Functions and Relations (Y11), Inequalities, Inequalities and Absolute Values, Linear Functions (Adv-2027) Tagged With: Band 2, num-title-ct-pathb, num-title-qs-hsc, smc-4385-10-Linear, smc-4385-50-Number line, smc-6214-08-Inequalities, smc-987-20-Inequalities

Functions, 2ADV F1 2006 HSC 1e

Solve  `3-5x <= 2`.  (2 marks)

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`x >= 1/5`

Show Worked Solution
`3-5x` `<= 2`
`-5x` `<= -1`
`x` `>= 1/5`

Filed Under: Further Functions and Relations (Y11), Inequalities, Inequalities and Absolute Values, Linear Functions (Adv-2027) Tagged With: Band 3, num-title-ct-pathb, num-title-qs-hsc, smc-4385-10-Linear, smc-6214-08-Inequalities, smc-987-20-Inequalities

Functions, 2ADV F1 2011 HSC 1e

Solve  `2 -3x <= 8`.   (2 marks)

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 `x>=-2`

Show Worked Solution
`2 -3x` `<= 8`
`-3x` `<= 6`
`x` `>= – 6/3`
`x` `>= -2`

Filed Under: Further Functions and Relations (Y11), Inequalities and Absolute Values, Linear Functions (Adv-2027) Tagged With: Band 3, smc-6214-08-Inequalities, smc-987-20-Inequalities

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