FUNCTIONS
REVISION
NOTES
1
,INDEX
Table of Contents
Front page .............................................................................................................................................. 1
Index ...................................................................................................................................................... 2
Functions Introduction .......................................................................................................................... 3
Linear Functions .................................................................................................................................... 4
Quadratic Functions .............................................................................................................................. 7
Hyperbolic Functions ........................................................................................................................... 10
Exponential Functions …………………………………………………………………………………………………………………...13
2
, FUNCTIONS INTRODUCTION
A function is a mathematical relationship between two variables, where every
input value has one output value
𝑥 = 𝑖𝑛𝑝𝑢𝑡 𝑜𝑟 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
𝑦 = 𝑜𝑢𝑡𝑝𝑢𝑡 𝑜𝑟 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
Domain: all the valid x=values of a graph
Range: all the valid y-values of a graph
Functional notation:
𝑓(𝑥) = 3𝑥
f(x) is used to represent the output value. (y-value)
f is used to name the function
(x) represents the x value that will be substituted
into the equation to calculate the y value for the
graph.
Decreasing and increasing functions:
▪ If the y- values get bigger as the x values get bigger – GRAPH IS INCREASING
▪ If the y- values become smaller as the x-values get bigger – GRAPH IS
DECREASING
Interval notation:
*Can be used for range, domain, and interpretation questions
[Can only be used to represent interval of real numbers)
E.g. (4;12)
This interval includes all real numbers greater than but not equal
to 4 and less than but not equal to 12
▪ Round brackets indicate the number is not included <>= )
▪ Round brackets always used for positive and negative infinity
▪ Square brackets indicate the number is included ≤≥ = ]
Functions can be represented as: Words, Mapping diagram, table, coordinates,
algebraic formula and in a graph.
Symmetrical axis are the lines that gives you a mirror image of the graph
3
REVISION
NOTES
1
,INDEX
Table of Contents
Front page .............................................................................................................................................. 1
Index ...................................................................................................................................................... 2
Functions Introduction .......................................................................................................................... 3
Linear Functions .................................................................................................................................... 4
Quadratic Functions .............................................................................................................................. 7
Hyperbolic Functions ........................................................................................................................... 10
Exponential Functions …………………………………………………………………………………………………………………...13
2
, FUNCTIONS INTRODUCTION
A function is a mathematical relationship between two variables, where every
input value has one output value
𝑥 = 𝑖𝑛𝑝𝑢𝑡 𝑜𝑟 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
𝑦 = 𝑜𝑢𝑡𝑝𝑢𝑡 𝑜𝑟 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
Domain: all the valid x=values of a graph
Range: all the valid y-values of a graph
Functional notation:
𝑓(𝑥) = 3𝑥
f(x) is used to represent the output value. (y-value)
f is used to name the function
(x) represents the x value that will be substituted
into the equation to calculate the y value for the
graph.
Decreasing and increasing functions:
▪ If the y- values get bigger as the x values get bigger – GRAPH IS INCREASING
▪ If the y- values become smaller as the x-values get bigger – GRAPH IS
DECREASING
Interval notation:
*Can be used for range, domain, and interpretation questions
[Can only be used to represent interval of real numbers)
E.g. (4;12)
This interval includes all real numbers greater than but not equal
to 4 and less than but not equal to 12
▪ Round brackets indicate the number is not included <>= )
▪ Round brackets always used for positive and negative infinity
▪ Square brackets indicate the number is included ≤≥ = ]
Functions can be represented as: Words, Mapping diagram, table, coordinates,
algebraic formula and in a graph.
Symmetrical axis are the lines that gives you a mirror image of the graph
3
