Worked example 2 (i) Create an input-output table for the function f (x) = x + 4, when the input values are {–2, –1, 0, 1, 2, 3} (ii) List the elements of the domain and range. (iii) List the couples.
Solution (i)
This is a function because each input has exactly one output.
In the above examples, we saw how to create an output from a given rule. However, if we have a list of the inputs and outputs, we can work backwards to fi nd the rule.
Discover the pattern of the function by asking: Then we write the rule as an equation.
Worked example 3
Find a relation (rule) that created the input-output table shown.
Input (x) 5
10 15 20
Solution What happened to the input to get the output?
Rule ?
Output (y) 9
14 19 24
Mapping functions
Another way to present input-output values is by drawing a mapping diagram. We ‘map’ the input to the output using arrows. A function must obey the following rule: There is exactly one output for each input value.
Section A Introducing concepts and building skills