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EXAMCOPY Functions, MET2 2022 VCAA 4

Consider the function , where

Part of the graph of is shown below.
 

  1. State the range of .   (1 mark)

  2.  i. Find .   (2 marks)

  3. ii. State the maximal domain over which is strictly increasing.   (1 mark)

  4. Show that .   (1 mark)

  5. Find the domain and the rule of , the inverse of .   (3 marks)

  6. Let be the function , where and .
  7. The inverse function of is defined by .
  8. The area of the regions bound by the functions and can be expressed as a function, .
  9. The graph below shows the relevant area shaded.
     

  1. You are not required to find or define .
  1. Determine the range of values of such that .   (1 mark)

  2. Explain why the domain of does not include all values of .   (1 mark)

Show Answers Only
a.    
b.i
b.ii
c.
d.
e.i 
e.ii No bounded area for
Show Worked Solution

a.   is the range.

b.i   
 
   
     
   
     

 
b.ii 

c.    
   

 
d.   To find the inverse swap and in

 
 
 
 
 
 
 

 
    Domain:
  

e.i   The vertical dilation factor of  is 

For ,

   [Using CAS]


♦♦♦♦ Mean mark (e.i) 10%.
MARKER’S COMMENT: Incorrect responses included and .

e.ii  When for  (or for  ) there is no bounded area.

  There will be no bounded area for .


♦♦♦♦ Mean mark (e.ii) 10%.