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Graphs, SPEC1 2012 VCAA 10

Consider the functions with rules    and 

    1. Find the maximal domain of     (1 mark)

    2. Find the maximal domain of     (1 mark)

    3. Find the largest set of values of    for which    is defined.   (1 mark)

  2. Given that    and that  , evaluate 

     

    Give your answer in the form     (3 marks)

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a.i.   

 
 

 
a.ii.   

♦♦ Mean mark part (a)(ii) 33%.

 
 
 

 

a.iii. 

♦♦ Mean mark part (a)(iii) 26%.

 
 

 

b.   
   

 

♦♦♦ Mean mark part (b) 20%.

 
 

Calculus, SPEC2 2018 VCAA 1

Consider the function  , where  .

  1. Determine the maximal domain and the range of  .  (2 marks)

  2. Sketch the graph of    on the axes below, labelling any endpoints and the -intercept with their coordinates.  (3 marks)


      

     
     

  3. Find    for  , expressing your answer in the form  .  (1 mark)

  4. Write down    for  , expressing your answer in the form  .  (1 mark)

  5. The derivative    can be expressed in the form  over its maximal domain.
  1. Find the maximal domain of  .  (1 mark)

  2. Find  , expressing your answer as a piecewise (hybrid) function.  (1 mark)

  3. Sketch the graph of  on the axes below.  (2 marks)


     

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a.   

 

 

b.   

 

c.   

 

 

d.   
   

 

e.i. 

♦♦ Mean mark part (e)(i) 21%.

 

e.ii. 

♦ Mean mark part (e)(ii) 49%, part (e)(iii) 48%.

 

e.iii.