Alg2 lesson 2.1
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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 document provides examples of relations and uses the vertical line test to determine if they are functions or not. It demonstrates identifying the domain and range and using function notation to evaluate outputs given inputs.
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Alg2 lesson 2.1
- 1. A relation pairs input values with output values.The set of input values (the independent variable) is called the domain.The set of output values (the dependent variable) is called the range.A relation is a function if 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 â 2, find f(-3)f(-3) = 5(-3) â 2 = -15 â 2 = -17As an ordered pair, the solution would be written (-3, -17)f(x) is another name for y