### About What is a Function in Math:

A relation is any set of ordered pairs (x,y). A function is a special type of relation where there is a one to one correspondence. Each first component or x value corresponds to or is linked to exactly one second component or y value. Many times we hear this read as 'for each x, there can be only one y'.

Test Objectives

- Understand the definition of a relation
- Understand the difference between domain and range
- Demonstrate the ability to determine if a relation represents a function

#1:

Instructions: Determine if each relation is a function, then list the domain and range.

a) {(3,2), (1,-7), (8,-6), (2,3), (0,5)}

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#2:

Instructions: Determine if each relation is a function, then list the domain and range.

a) {(6,3), (1,7), (6,-2)}

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#3:

Instructions: Determine if each relation is a function, then list the domain and range.

a) {(-1,0), (-2,3), (7,-8), (1,0)}

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#4:

Instructions: Determine if each relation is a function, then list the domain and range.

a) {(-20,5), (32, 10), (-20,7), (8,6)}

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#5:

Instructions: Determine if each relation is a function, then list the domain and range.

a) {(-3,5), (7,-1), (0,15), (6,2)}

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Written Solutions:

#1:

Solutions:

a) Yes - this relation is a function

domain = {3,1,8,2,0}

range = {2,-7,-6,3,5}

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#2:

Solutions:

a) No - this relation is not a function

domain = {6,1}

range = {3,7,-2}

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#3:

Solutions:

a) Yes - this relation is a function

domain = {-1,-2,7,1}

range = {0,3,-8}

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#4:

Solutions:

a) No - this relation is not a function

domain = {-20,32,8}

range = {5,10,7,6}

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#5:

Solutions:

a) Yes - this relation is a function

domain = {-3,7,0,6}

range = {5,-1,15,2}