Question

tek a.1.2a? domain, range, and functions
example problem 2: graph interpretation
use the scatter plot below to answer the following questions.
questions:

1. list the domain and range of the relation. domain = 3 range = 5
2. does this graph represent a function? explain your reasoning.
3. what test can you use to determine if it?s a function? apply it to this graph.

Explanation:

Step1: Identify domain values

The domain is the set of all x - values. The x - values in the points \((1,5)\), \((1,2)\), \((2,3)\), \((3,4)\) are \(1\), \(2\), \(3\). So the domain is \(\{1, 2, 3\}\).

Step2: Identify range values

The range is the set of all y - values. The y - values in the points \((1,5)\), \((1,2)\), \((2,3)\), \((3,4)\) are \(2\), \(3\), \(4\), \(5\). So the range is \(\{2, 3, 4, 5\}\).

Step3: Determine if it's a function

A function has exactly one output (y - value) for each input (x - value). Here, when \(x = 1\), there are two y - values (\(y=2\) and \(y = 5\)). So it is not a function.

Step4: Apply the vertical - line test

The vertical - line test states that if any vertical line drawn on the graph of a relation intersects the graph at more than one point, the relation is not a function. A vertical line \(x = 1\) intersects the scatter - plot at two points \((1,2)\) and \((1,5)\), so it is not a function.

Answer:

1. Domain: \(\{1, 2, 3\}\), Range: \(\{2, 3, 4, 5\}\)
2. No. Because when \(x = 1\), there are two different y - values (\(y = 2\) and \(y=5\)).
3. The vertical - line test. A vertical line \(x = 1\) intersects the graph at two points \((1,2)\) and \((1,5)\), so it is not a function.