Initial Diagnostic Audit - Unit G4: Functions
Section G4.1 - Functions, Mappings and Domains

1.
The function f is defined by f : xx3 - x for all x.

(a) What is f(1)?   
(b) What is f(-1)?   
(c) Is f a 1 : 1 mapping?   


2.
The function f(x) = 
x4 - 16
x - 2

(a) What is the value of f(-4)?   

(b) What is the value of x for which f(x) = 0?   

Section G4.2 - Composite Functions
3. The functions f and g are defined by

f : x → 
x - 1
     g : x → 
x
     (x ≠ -1)
x + 1
2

(a)   f(2) =  
  

(b)   g
1
3
  =  
  

(c)   gf(2) =  
  

(d)   fg(2) =  

4. f : xx + 2 and g : xx - 2

Does fg(x) = gf(x) for all x?   

Section G4.3 - Inverse Functions
5. The functions f and g are defined by

f : x → 2x + 1      g : x → 
1
(x - 1)
2

(a)   fg(1) =

(b)   gf(1) =

(c)   Are f and g inverse functions?

6. The function f is defined by

f(x) = 
3x + 2
     (x ≠ 1)
x - 1

and its inverse is of the form

f -1(x) = 
ax + 2
x + b

when a and b are constants.

(a)   a =

(b)   b =

Section G4.4 - Transformations of Graphs of Functions
7. The graph below illustrates the function y = f(x) by a dashed line.

What are the equations of the other functions?

(a) Function A   y = f ()

(b) Function B   y = f ()

(c) Function C   y = f ()

8. The graph of y = cosx for 0° ≤ x ≤ 360° is given below.

Give the equation of each of the transformed graphs.
In each case the graph of y = cosx is shown dotted to help you.

(a)  y =

(b)  y =


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Produced by Russell Geach for CIMT - January 2014