SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Functions, 2ADV F1 2020 HSC 24

The circle of  `x^2-6x + y^2 + 4y-3 = 0`  is reflected in the `x`-axis.

Sketch the reflected circle, showing the coordinates of the centre and the radius.  (3 marks)

Show Answers Only

Show Worked Solution
`x^2-6x + y^2 + 4y-3` `= 0`
`x^2-6x + 9 + y^2 + 4y + 4-16` `= 0`
`(x-3)^2 + (y + 2)^2` `= 16`

 
`=>\  text{Original circle has centre (3, − 2), radius = 4}`

`text(Reflect in)\ xtext(-axis):`

♦ Mean mark 48%.

`text{Centre (3, − 2) → (3, 2)}`
 

Functions, 2ADV F1 SM-Bank 36

Consider the function  `f(x) = 1/(x + 2)`.
 

 
 

  1. Sketch the graph  `y = f(−x)`.   (2 marks)

  2. On the same graph, sketch  `y = −f(x)`.   (2 marks)

Show Answers Only

i.

ii.   

Show Worked Solution

i.   `text(Sketch)\ \ y = 1/(x + 2)`

`y = f(−x) \ =>\ text(reflect)\ \ y = 1/(x + 2)\ \ text(in the)\ ytext(-axis).`
 

 

ii.   `y = −f(x) \ =>\ text(reflect)\ \ y = 1/(x + 2)\ \ text(in the)\ xtext(-axis).`