Question

instructions
use the set of ordered pairs to answer the questions.
classify ordered pairs
set of ordered pairs
{(0,2),(3,4),(-3,-2),(2,4)
16 multiple answer 2 points
select all that apply
□ d: -3, 3
□ discrete
□ the domain is {-3, 0, 2, 3}
□ function
□ linear
□ the range is {-2, 2, 4}
□ r: -2, 2
□ not a function

Explanation:

Step1: Analyze Domain

The domain of a set of ordered pairs \((x,y)\) is the set of all \(x\)-values. For the set \(\{(0,2),(3,4),(-3,-2),(2,4)\}\), the \(x\)-values are \(0, 3, -3, 2\). So the domain is \(\{-3, 0, 2, 3\}\), so "The Domain is \(\{-3,0,2,3\}\)" is correct. The interval \([-3,2]\) includes all real numbers between -3 and 2, but our domain has discrete points (3 is outside \([-3,2]\)), so \(D:[-3,2]\) is incorrect.

Step2: Check Discrete

Since the ordered pairs represent individual points (not a continuous interval), the relation is discrete. So "discrete" is correct.

Step3: Check Function

A function is a relation where each input (x - value) has exactly one output (y - value). Here, each \(x\)-value (\(0, 3, -3, 2\)) has only one \(y\)-value, so it is a function. Thus, "function" is correct, and "not a function" is incorrect.

Step4: Analyze Linear

A linear relation has a constant rate of change (slope). Let's check the slopes between points:

• Between \((0,2)\) and \((3,4)\): slope \(m=\frac{4 - 2}{3 - 0}=\frac{2}{3}\)
• Between \((3,4)\) and \((2,4)\): slope \(m=\frac{4 - 4}{2 - 3}=0\)
• Between \((2,4)\) and \((-3,-2)\): slope \(m=\frac{-2 - 4}{-3 - 2}=\frac{-6}{-5}=\frac{6}{5}\)

Since the slopes are not constant, it is not linear. So "linear" is incorrect.

Step5: Analyze Range

The range is the set of all \(y\)-values. The \(y\)-values are \(2, 4, -2, 4\), so the range is \(\{-2, 2, 4\}\) (we remove duplicates). So "The Range is \(\{-2,2,4\}\)" is correct. The interval \(R:[-2,2]\) includes all real numbers between -2 and 2, but our range has 4 which is outside \([-2,2]\), so \(R:[-2,2]\) is incorrect.

Answer:

• discrete
• The Domain is \(\{-3,0,2,3\}\)
• function
• The Range is \(\{-2,2,4\}\)