Question

1. given the graph

a. draw a mapping of that relation
b. create a table of that relation
c. state the domain
d. state the range

Explanation:

Step1: Identify Points from Graph

From the graph, the points are: \((-4, 0)\), \((-1, 2)\), \((2, 3)\), \((3, 0)\) (assuming the x - axis labels and point positions: let's parse the x - axis. The first point is at x=-4, y = 0; second at x=-1, y = 2; third at x = 2, y = 3; fourth at x=3, y = 0).

Step2: Part a - Mapping Diagram

• Domain Set (x - values): \(\{-4, -1, 2, 3\}\)
• Range Set (y - values): \(\{0, 2, 3\}\)
• In a mapping diagram, we draw arrows from each element in the domain to its corresponding element in the range. So:
• \(-4\) maps to \(0\)
• \(-1\) maps to \(2\)
• \(2\) maps to \(3\)
• \(3\) maps to \(0\)

Step3: Part b - Table of Relation

We create a table with two columns: \(x\) (input) and \(y\) (output).

\(x\)	\(y\)
\(-1\)	\(2\)
\(2\)	\(3\)
\(3\)	\(0\)

Step4: Part c - Domain

The domain of a relation is the set of all \(x\) - values (input values) of the ordered pairs. From the points \((-4, 0)\), \((-1, 2)\), \((2, 3)\), \((3, 0)\), the domain is the set of \(x\) - coordinates. So domain \(=\{-4, -1, 2, 3\}\)

Step5: Part d - Range

The range of a relation is the set of all \(y\) - values (output values) of the ordered pairs. From the points \((-4, 0)\), \((-1, 2)\), \((2, 3)\), \((3, 0)\), the range is the set of \(y\) - coordinates. So range \(=\{0, 2, 3\}\)

Answer:

Part a:

• Domain: \(\{-4, -1, 2, 3\}\)
• Range: \(\{0, 2, 3\}\)
• Mapping: Draw arrows from \(-4\) to \(0\), \(-1\) to \(2\), \(2\) to \(3\), \(3\) to \(0\) between the domain and range sets.

Part b:

\(x\)	\(y\)
\(-1\)	\(2\)
\(2\)	\(3\)
\(3\)	\(0\)

Part c:

Domain: \(\{-4, -1, 2, 3\}\)

Part d:

Range: \(\{0, 2, 3\}\)