Answer:
--- Function A
--- Function B
--- Function C
Step-by-step explanation:
Solving (a): Equation of Function A
An exponential equation is represented as:

From the graph of function A,


For: 
becomes



For: 
becomes


Substitute 1 for a



becomes


Replace y with f(x)

Solving (b): Equation of Function B
A quadratic equation is represented as:

From the table of function B,



For: 
becomes



For 
becomes



For 
becomes



So, we solve for a, b and c in:



Make c the subject in 

Substitute
in
and 
becomes

Collect Like Terms


Divide through by 2


becomes

Collect Like Terms


Divide through by 3

Solve for a and b in:
and 
Subtract both equations:



Divide both sides by -1


Substitute 1 for a in 


Subtract 9 from both sides



Substitute
and
in 



So, the equation is:



Replace y with f(x)

Solving (c): Equation of Function C
This is calculated using:

Where
-- the first term
d = the difference between successive terms


So, we have:


Open bracket

Collect Like Terms

