Unit 1

Functions

Writing Domain and Range Intervals

On the previous page, you saw a domain written as {x|x ≥ 0, x$\in$R}.  This is called "set builder notation".  When something is enclosed in  { }, it is referring to a set of values.  The x before the | symbol lets you know the set will include all x-values that obey the rule behind the |.  There are two rules in this case, x ≥ 0 and  x$\in$R.  So any value that is both real and greater than or equal to zero is included in this set.

Take a look at the range {y |y = 0.5n , n$\in$N}.  This time there are y-values that follow the rules after the |.  In this case, y can be any value found by entering a natural number into the expression 0.5n.  So y can be 0.5, 1, 1.5, 2... .

An alternative method for writing an interval uses "interval notation".  In this method an upper and lower limit are listed and square and round brackets show whether the endpoint is included.  For example, $[0,\infty )$ shows that values from zero to infinity are included.  The endpoint of 0 is also included because there is a square bracket beside it and the endpoint of infinity is not included because a round bracket is used.  A round bracket is always used with the infinity symbol. 

If you want to indicate multiple disjoint intervals, you can use the union symbol $\cup$.  So [−3,2]$\cup$(5,9) means all values from −3 to 2 are included and all values from 5 to 9 are included.  The −3 and 2 are included in this set, but the 5 and the 9 are not.