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Functions, MET1 EQ-Bank 2

Consider the functions and , where

  1. State the range of .  (1 mark)

  2. Determine the rule for the equation and state the domain of the function .  (2 marks)

  3. Let be the function .
  4. Determine the maximal domain, , such that exists.  (1 marks)

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a.   

b.   

c.   

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a.   

b.    
   
   

c.    
   

Calculus, MET2 2023 VCAA 1

Let . Part of the graph of is shown below.

  1. State the coordinates of all axial intercepts of .   (1 mark)
  2. Find the coordinates of the stationary points of .   (2 marks)
    1. Let .
    2. Find the values of for which .   (1 mark)
    1. Write down an expression using definite integrals that gives the area of the regions bound by and .  (2 marks)
    2. Hence, find the total area of the regions bound by and , correct to two decimal places.   (1 mark)
  1. Let , where and .
  2. Find the possible values of and .   (4 marks)
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a.   

b.   

c.i. 

c.ii.

 

c.iii.

d.  

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a.   
  

b.   


  

ci   

  

cii  


  

ciii 
 

  

d.   

  

 

Functions, MET1 2017 VCAA 7

Let  .

  1.  State the range of .   (1 mark)

  2.  Let  .
    1. Find the largest possible value of such that the range of is a subset of the domain of .   (2 marks)

    2. For the value of found in part b.i., state the range of .   (1 mark) 

  3. Let  .
  4. State the range of .   (1 mark)

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a. 
 

 

b.i. 

♦ Mean mark 38%.
 


 


 

b.ii. 

♦♦♦ Mean mark 20%.


 

c. 

♦♦ Mean mark 30%.
 
 

 

Graphs, MET1 2016 VCAA 5

Let  , where    and  , where  .

  1.   i. Find the rule for , where  .   (1 mark)

    ii. State the domain and range of .   (2 marks)

  2. iii. Show that  .   (2 marks)

  3. iv. Find the coordinates of the stationary point of and state its nature.   (2 marks)

     

  4. Let    where  .
  5.  i. Find the rule for  .   (2 marks)

  6. ii. State the domain and range of  .   (2 marks)

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  1.   i.
  2.  ii.
  3. iii.
  4. iv.
  5.  i.
  6. ii.
  7.    
Show Worked Solution
a.i.   
   

 

a.ii.  

♦♦ Mean mark part (a)(ii) 30%.
 
 

 

MARKER’S COMMENT: Many students were unsure of how to present their working in this question. Note the layout in the solution.
a.iii.  
   
   
   

 

 

 

 

a.iv.  

♦ Mean mark part (a)(iv) 41%.
MARKER’S COMMENT: Solving a fraction is zero

   

 

 

b.i.  

♦ Mean mark (b)(i) 49%.
MARKER’s COMMENT: Many students failed to consider the restrictions on the domain in and only select the negative root.

 

 

♦ Mean mark part (b)(ii) 44%.

 

b.ii.  

 

Functions, MET1 2008 VCAA 10

Let  .

  1. Find the rule and domain of the inverse function  .   (2 marks)

  2. On the axes provided, sketch the graph of    for its maximal domain.   (1 mark)


     

    met1-2008-vcaa-q2
     

  3. Find    in the form    where , and are real constants.   (2 marks)

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  2.  
    met1-2008-vcaa-q10-answer
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a.  

 

 


  

b.  

♦ Mean mark part (b) 19%.
MARKER’S COMMENT: Few students were aware that a function of its own inverse function is the line    over the appropriate domain.

met1-2008-vcaa-q10-answer

 

♦ Mean mark 34%.
c.   
 
   
   
   

Functions, MET1 2011 VCAA 4

If the function has the rule    and the function has the rule  

  1.  find integers and such that    (2 marks)

  2.  state the maximal domain for which  is defined.   (2 marks)

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a.  
   
   

 
 

 

b.   

♦♦♦ Mean mark 13%.
MARKER’S COMMENT: “Very poorly answered” with a common response of that ignored the information from part (a).


 

 vcaa-2011-meth-4ii