Question

which relation is a function?
show your work here
○ $(-1,4),(0,1),(-1,-2),(2,-5)$
○ $(0,0),(1,1),(2,1),(2,2)$
○ $(-1,4),(0,0),(1,4),(1,-4)$
○ $(-2,0),(0,-2),(2,2),(4,-2)$

Explanation:

Step1: Recall the definition of a function

A relation is a function if every input (x - value) has exactly one output (y - value). So we need to check each option for repeated x - values with different y - values.

Step2: Analyze Option 1: \((-1,4),(0,1),(-1,-2),(2,-5)\)

The x - value \(-1\) is paired with \(y = 4\) and \(y=-2\). Since one input (\(-1\)) has two different outputs, this relation is not a function.

Step3: Analyze Option 2: \((0,0),(1,1),(2,1),(2,2)\)

The x - value \(2\) is paired with \(y = 1\) and \(y = 2\). Since one input (\(2\)) has two different outputs, this relation is not a function.

Step4: Analyze Option 3: \((-1,4),(0,0),(1,4),(1,-4)\)

The x - value \(1\) is paired with \(y = 4\) and \(y=-4\). Since one input (\(1\)) has two different outputs, this relation is not a function.

Step5: Analyze Option 4: \((-2,0),(0,-2),(2,2),(4,-2)\)

Check each x - value:

• For \(x=-2\), the output is \(y = 0\) (only one output).
• For \(x = 0\), the output is \(y=-2\) (only one output).
• For \(x = 2\), the output is \(y = 2\) (only one output).
• For \(x = 4\), the output is \(y=-2\) (only one output).

No x - value is repeated with different y - values, so this relation is a function.

Answer:

\((-2,0),(0,-2),(2,2),(4,-2)\) (the last option)