UNIT 4 Equivalent forms


In this unit you will: • determine, interpret and justify equivalence of different forms of the same relationship or rule.


Equivalent forms of representing functions and relationships


There is often more than one way to describe or represent a relationship. We call these equivalent forms.


Consider the sequence of numbers in Table 2 below. Table 2 A simple sequence


Term number Term value


T1 1


Verbal descriptions


One way to describe the sequence in Table 2 in words is as follows: • To get the next term, add 3, then add 5. In other words, add two more each time.


So, the next three terms are 9 + 7 = 16; 16 + 9 = 25; 25 + 11 = 36


• Another way of describing this number pattern in words is as follows: The pattern is 12; 22; 32; … . So, the next three terms are 42 = 16; 52 = 25; 62 = 36. Do you see that, although the reasoning is different, we end up with the same sequence?


Remember


As well as verbal descriptions such as these, we can also describe the same relationship or rule using flow diagrams, tables, formulae and equations.


Equivalent descriptions of the same rule are descriptions that look different, but that have the same meaning.


T2 4


T3 9


T4 16


132 Chapter 4: Patterns, functions and relationships


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