A relation pairs input values (the domain) with output values (the range). A relation is a function if each input maps to exactly one output. The first example relation is a function because each input in the domain {-3, 1, 3, 4} maps to only one output in the range {3, 1, -2}. The second example is not a function because the input 1 maps to both -2 and 1 in the range. The vertical line test can also determine if a relation is a function by checking if any vertical line passes through more than one point.

1. A relationpairs input values with output values.The set of inputvalues (the independent variable) is called the domain.The set of output values (the dependent variable) is called the range.A relation is a functionif there is exactly one output for each input.It is NOT a function if any input has more than one outputRelations

2. Identify the Domain and Range. Then tell if the relation is a function.InputOutput-3 3 1 1 3 -2 4 Function?Yes: each input is mappedonto exactly one outputDomain = {-3, 1,3,4}Range = {3,1,-2}

3. Identify the Domain and Range. Then tell if the relation is a function.InputOutput-3 3 1 -2 4 1 4Domain = {-3, 1,4}Range = {3,-2,1,4}Function?No: input 1 is mapped onto Both -2 & 1

4. InputOutput-3 31 14 -2 4(4,4)(-3,3)(1,1)(1,-2)

5. Vertical Line TestSlide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line.If there are not two points on the same vertical line then the relation is a function.If there are two points on the same vertical line then the relation is NOT a function

6. Use the vertical line test to visually check if the relation is a function.(4,4)(-3,3)(1,1)(1,-2)Function?No, Two points are on The same vertical line.

7. Use the vertical line test to visually check if the relation is a function.Function?Yes, no two points are on the same vertical line

8. Function NotationIf f(x) = 5x – 2, find f(-3)f(-3) = 5(-3) – 2 = -15 – 2 = -17As an ordered pair, the solution would be written (-3, -17)f(x) is another name for y