Set notation EMA43
Examples:
fx:x 2 R; x > 0 g The set of allx-values such thatxis an element of the set of real numbers and
is greater than 0.
fy:y 2 N; 3 < y 5 g The set of ally-values such thatyis a natural number, is greater than 3 and is
less than or equal to 5.
fz:z 2 Z; z 100 g The set of allz-values such thatzis an integer and is less than or equal to 100.
Interval notation EMA44
It is important to note that this notation can only be used to represent an interval of real numbers.
Examples:
(3; 11) Round brackets indicate that the number is not included. This interval includes all real
numbers greater than but not equal to 3 and less than but not equal to 11.
( 1; 2) Round brackets are always used for positive and negative infinity. This interval includes
all real numbers less than, but not equal to 2.
[1; 9) A square bracket indicates that the number is included. This interval includes all real
numbers greater than or equal to 1 and less than but not equal to 9.
Function notation EMA45
This is a very useful way to express a function. Another way of writingy= 2x+ 1isf(x) = 2x+ 1. We say
“fofxis equal to 2 x+ 1”. Any letter can be used, for example,g(x),h(x),p(x), etc.
1.Determine the output value:
“Find the value of the function forx= 3 ” can be written as: “findf( 3)”.
Replacexwith 3:f( 3) = 2( 3) + 1 = 5
)f( 3) = 5This means that whenx= 3 , the value of the function is 5.
2.Determine the input value:
“Find the value ofxthat will give ay-value of 27” can be written as: “findxiff(x) = 27”.
We write the following equation and solve forx:2 x+ 1 = 27
)x=13This means that whenx= 13the value of the function is 27.Representations of functions EMA46
Functions can be expressed in many different ways for different purposes.
Chapter 6. Functions 147