Lesson: Domain and Range

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Lesson: Domain and Range
The domain is the set of all of the first elements (x values) and the range is the set of all of
the second elements (y values)
We can use set notation or interval notation to describe the domain and range.
Set notation may be written in different ways depending on the author and the publisher.
In this case, we could write the domain as:
SET NOTATION
Domain: {1,2,3}
x  {1, 2, 3}
{x: x  N, 1 ≤ x ≤ 3}
or {x| x  N, 1 ≤ x ≤ 3}
or {x:1 ≤ x ≤ 3, x  N}
My preference is as follows… If you can list the values (if there is a finite amount in the set)
then LIST THEM. If there is an infinite amount, then use set notation.
Thus, in the above example
x  {1, 2, 3}
y  {1, 2, 3}
Example:
State the domain and range using formal notation
{x: x  R}
{y: y  R}
x and y can be ANYTHING in eth real number system .. no restrictions
Example:
State the domain and range using formal notation
x can be anything and thus no restrictions
{x: x  R}
y has restrictions .. it must be above 2 {y: y  R, y ≥ 2}
x has restrictions
{x: x  R, x ≥ 1}
y has no restrictions {y: y  R}
x has restrictions
{x: x  R, -3 ≤ x ≤ 2}
y has restrictions {y: y  R, -5 ≤ y ≤ 5}
Example:
1. State the domain and range of each of the following using formal notation
x has restrictions
{x: x  R, -2 ≤ x ≤ 2}
y has restrictions {y: y  R, -2 ≤ y ≤ 2}
2. State the domain and range of each of the following using formal notation
x has no restrictions
{x: x  R}
y has restrictions {y: y  R, y ≤ 2}
3. State the domain and range of each of the following using formal notation
x has no restrictions
{x: x  R}
y has no restrictions {y: y  R}
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