80 Domain Using Union Update

Because the domain refers to the set of possible input values the domain of a graph consists of all the input values shown on the x axis.

Domain using union. A subset of the number line consisting of two or more intervals is written using the set union symbol cup. Find the domain and range of f x 2x 3 x. An example of a function s domain in interval notation is 3 4.

However the break in the domain means that we must use our union symbol u between our 2 domain pieces. Infinity 2 u 3 infinity remember that infinity is always noninclusive and the u means that both pieces of the graph are part of the possible domain. Finding the domain and range using toolkit functions.

An example of a range with a union is 3 2 u 5 9. There are no restrictions on the domain as any real number may be cubed and then subtracted from the result. Here is our final domain.

For example the set of all real numbers lying at least one unit from 0 but less than two units from zero written in interval notation is 2 1 cup 1 2. The union sign indicates that there is a break in the functions domain and range. Use the union symbol cup to combine all intervals into one set.