By the end of this section you should: ● understand what a function is
When we were working with linear patterns in Unit 7, we saw that if we were to draw a graph of the pattern, it would always be a straight line. This is also known as a linear function.
● ●
● be able to work with functions and the formulae associated with them
We now have several ways to fi nd the unknown value in a linear equation (also known as a linear function): ●
Create a word equation, and substitute in values to solve for an answer Create a table and fi nd the missing value
Draw a graph and read information from the graph Writing function relations for input-output tables
A linear function is a mathematical expression which, when graphed, will form a straight line.
A linear function is very like a linear pattern. There is always a relation (rule). This relation can be written as an equation. Each stage of the function can be predicted by this relation.
When dealing with functions, we don’t use the word ‘stage’. It is more mathematically correct to use the words ‘input’ and ‘output’.
Worked example 1 Recall the function machine from 9.5.
The relation states that any number that is put in (the input) is multiplied by 12, and the result is the output. (i) What would be the output for the following numbers? (a) 1
(b) 2
Solution (i)
(c) 3 (ii) Is this a linear function (pattern)? (d) 4 (e) 5 Input IN 12x OUT Output
Worked example 2 The function machine performs the following: output = 4 times the input + 2
Find the output value for each of the following inputs. (i) Input = 5
(ii) Input = 6 (iii) Input = 8 Input IN 4x + 2 OUT Output
(i) (ii) (iii)
Remember to use the correct order of operations.
Solution
Section A Introducing concepts and building skills