Extension 5.1 Relations and Functions Lesson Tutorials A relation pairs inputs with outputs. A relation that pairs each input with exactly one output is a function. Key Vocabulary relation, p. 208 Vertical Line Test, p. 209 EXAMPLE Determining Whether Relations are Functions 1 Determine whether each relation is a function. COMMON CORE a. (−2, 2), (−1, 2), (0, 2), (1, 0), (2, 0) Functions Every input has exactly one output. In this extension, you will ● determine whether relations are functions. ● use the vertical line test to determine whether a graph represents a function. Learning Standards: 8.F.1 F.IF.1 F.IF.5 So, the relation is a function. b. Input −2 −1 0 0 1 2 3 4 5 6 7 8 Output The input 0 has two outputs, 5 and 6. So, the relation is not a function. c. Input Output −9 −2 5 12 0 5 10 Every input has exactly one output. So, the relation is a function. Determine whether the relation is a function. 1. (−5, 0), (0, 0), (5, 0), (5, 10), (10, 10) 2. Input Output 2 2.6 4 5.2 6 7.8 3. Input 1 2 — Output 1 4 −— 0 1 4 — Determine whether the statement is true or false. Explain your reasoning. 4. Every function is a relation. 5. Every relation is a function. 6. When you switch the inputs and outputs of any function, the resulting relation is a function. 7. REASONING You record the number x of runs scored by the winning team and the number y of runs scored by the losing team for each softball game in a team’s season. Does the relation necessarily represent a function? Explain. 208 Chapter 5 MSCA_ALG1_PE_0501_ext.indd 208 Linear unctions F 12/17/13 1:54:59 PM You can use a vertical line test to determine whether a graph represents a function. Vertical Line Test A graph represents a function when no vertical line passes through more than one point on the graph. Words Examples Function Not a function y y x Using the Vertical Line Test 2 EXAMPLE x Determine whether each graph represents a function. a. b. y 6 y 6 5 5 4 4 3 3 2 2 1 1 0 0 1 2 3 4 5 6 0 7 x You can draw a vertical line through (2, 2) and (2, 5). 0 1 2 3 4 5 6 7 x No vertical line can be drawn through two points on the graph. So, the graph does not represent a function. So, the graph represents a function. Determine whether the graph represents a function. 8. y 6 9. y 6 10. y 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 1 2 3 4 5 6 7 x 0 1 2 3 4 5 6 7 x 0 0 1 2 3 4 5 6 7 x 11. REASONING You studied linear equations in Chapter 2. Do all linear equations represent functions? Explain your reasoning. Extension 5.1 Relations and Functions 209

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