Use Set-builder Notation to Describe the Following Sets

We can write the domain of fx in set builder notation as x x 0. Using Interval Notation.

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In this section we will explore various ways to express different sets of numbers inequalities and absolute value inequalities.

. If the domain of a function is all real numbers ie. Positive and negative whole numbers. We can use a number line as shown in Figure 2.

There is also a subtle variation on set builder notation. Here is an example. The blue ray begins at x 4 x 4 and as indicated by the arrowhead continues to infinity.

As stated above we can use set-builder notation to express the domain of a function. If we are given an equation or graph we might use inequalities or intervals to describe domain and range. While the condition is generally given after the such that sometimes it is hidden in the first part.

For example the function. In this section we will introduce the standard notation used to define sets and give you a chance to practice writing sets in three ways inequality notation set-builder notation and interval notation. The set Z is the set of integers.

Has domain that consists of all real numbers greater than or equal to zero because the square root of a negative number is not a real number. List a few elements in the sets below and describe them in words. Indicating the solution to an inequality such as x 4 x 4 can be achieved in several ways.

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