Question

What is the domain and range (use set notation)​

Answer 1

x = -1, 2, 3

Explanation:

There are only 3 x-values in the domain of this function because there are only 3 points where the function is defined.

These points occur when x = -1, x = 2, and x = 3.

We can represent these x-values in set notation as:

D = x

This reads: "The domain of the function is a variable x such that x equals -1, 2, or 3."

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Note that you could also add that x is an element of all real numbers before the "such that" statement. This would be denoted:

D = x ∈ R

This set reads: "The domain of the function is a variable x that is a set of all real numbers such that x equals -1, 2, or 3."

Answer 2

Domain: {-1, 2, 3}

Range: {-4, 3}

Explanation:

The diagram shows a Cartesian plane with (x, y) points:

• (-1, -4)
• (2, 3)
• (3, -4)

Domain

The domain is the set of x-values.

The x-values of the plotted points are -1, 2 and 3.

Therefore, the domain in set notation is:

`\large\boxed{\textsf{Domain:} \quad \{-1, 2, 3\}}`

Range

The range is the set of y-values.

The y-values of the plotted points are -4, 3 and -4.

Therefore, the range in set notation is:

`\large\boxed{\textsf{Range:} \quad \{-4, 3\}}`

`\hrulefill`

Note: Sets are defined by unique elements, and duplicates are not included. Therefore, in set notation, the repetition of elements is not necessary.