How to Identify Relations and Functions? (+FREE Worksheet!)

Relations and Functions – Example 1:

Relations and Functions – Example 2:

Relations and Functions – Example 3:

Relations and Functions – Example 4:

Solution:

The relation is not a function. Input 9 has two outputs: 15 and 22. Remember that in a function, the input value must have one and only one value for the output.

The domain is all the \(x\)-coordinates: {1, 6, 9, 11}

The domain is all the \(y\)-coordinates: {5, 15, 16, 22, 25}

Exercises for Identifying Relations and Functions

Determine if the following relations are functions. Then state the domain and range.

1) g={(1, 5), (2, 6), (3, 7), (5, 10), (6, 20), (10, 35)}

2)

3)

4) f={(-2, 3), (7, 5), (5, -4), (-2, 10), (10, 15)}

1)The relation is a function.

The domain is all the \(x\)-coordinates: {1, 2, 3, 5, 6, 10}

The domain is all the \(y\)-coordinates: {5, 6, 7, 10, 20, 35}

2)The relation is not a function. Input -10 has two outputs: -2 and 3.

The domain is all the \(x\)-coordinates: {-10, -5, 0, 5, 15}

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The domain is all the \(y\)-coordinates: {-2, 0, 5, 12, 3, 20}

3)The relation is not a function. Input 7 has two outputs: 15 and 18.

The domain is all the \(x\)-coordinates: {5, 6, 7}

The domain is all the \(y\)-coordinates: {15, 16, 17, 18}

4)The relation is not a function. Input -2 has two outputs: 3 and 10.

The domain is all the \(x\)-coordinates: {-2, 7, 5, 10}

The domain is all the \(y\)-coordinates: {3, 5, -4, 10, 15}

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