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Functions and Graphs, SMB-001

`f(x)` is defined by the equation  `f(x)=3-x^2`.

  1. Find the coordinates of the `x`-intercepts of `f(x)`.  (1 mark)

  2. State the domain and range of `f(x)`.   (2 marks)

Show Answers Only

i.    `(sqrt3,0) and (-sqrt3, 0)`

ii.    `text{Domain: all}\ x`

`text{Range}\ f(x): \ y<=3`

Show Worked Solution

i.    `xtext{-intercepts occur when}\ y=0`

`3-x^2` `=0`  
`x^2` `=3`  
`x` `=+-sqrt3`  

 
`:. xtext{-intercepts at} (sqrt3,0) and (-sqrt3, 0)`
 

ii.   `text{Domain: all}\ x`

`text{Find range}\ f(x):`

`x^2>=0\ text{for all}\ x \ \ => \ \ 3-x^2<=3\ text{for all}\ x`

`:.\ text{Range}\ f(x): \ y<=3`