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5 Ways to Determine if a Relation is a Function

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montgomery-arjun
28 diapositives · 466 Views · Oct 26, 2014

Understanding the difference between a relation and a function is essential in mathematics. A relation is a set of input-output pairs where each input can correspond to multiple outputs. In contrast, a function assigns exactly one output for each input. This guide presents five methods to determine if a relation is a function: mapping input-output pairs, creating an X-Y table (T-table), analyzing ordered pairs, applying the vertical line test on graphs, and constructing a function table. Each method helps clarify the essential criteria for identifying functions.

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5 Ways to Determine if a Relation is a Function
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  1. 5 WAYS to determine if a Relation is a Function

  2. Relation- a set of input values and output values, often written as ordered pairs (where x is input and y is output)

  3. Relation- a set of input values and output values, often written as ordered pairs (where x is input and y is output)* NOTevery relation is a function.

  4. Relation - a set of input values and output values, often written as ordered pairs (where x is input and y is output)* NOTevery relation is a function.Function - a rule that assigns each input to exactly oneoutput.

  5. Relation - a set of input values and output values, often written as ordered pairs (where x is input and y is output)* NOTevery relation is a function.Function - a rule that assigns each input to exactly oneoutput. For every x there is one, and only one, y.

  6. Relation - a set of input values and output values, often written as ordered pairs (where x is input and y is output)* NOTevery relation is a function.Function - a rule that assigns each input to exactly oneoutput. For every x there is one, and only one, y.* EVERY function IS a relation.

  7. Function What is the difference in a relation and a function? Relation

  8. There are 5 ways to determine if a Relation is a Function One way is called: Mapping Input Output 2 3 4 4 6 6 8

  9. This mapping shows each input value and its corresponding output value. This is NOT a function. Why? Input Output 2 3 4 4 6 6 8 The input “2” has more than one output.

  10. Is this a function? Input Output 1 2 0 3 Yes, the inputs have only one output.

  11. Another way is called: an X Y Table (T-table) Input Output 2 3 4 6 6 8

  12. Is this a function? x y 0 1 • 3 2 5 Yes, each input has only one output!

  13. Another way is called: Ordered PairsIs this relation a function? (3,1), (5,3), (2,8), (6,8) Yes, each input (x) has only one output (y)! None of the x’s are repeated!

  14. Is this relation a function? (5,8), (3,7), (1,6), (5,4) No, the input 5 has two outputs!

  15. Is this relation a function? (5,8), (3,7), (1,6), (3,7) Yes, the input 3 alone isn’t repeated, the output that goes with it was repeated too. Remember the rule, each input can have only one output. The only output for 3 is 7.

  16. Another way is by graphing and using the Vertical Line TestIs this a function? No, because the input 2 has two outputs. Draw a vertical line to check.

  17. Is this a function? Yes, because each input has only one output. Draw vertical lines to check.

  18. Is this a function? No, because the input, 3, has infinite outputs.

  19. Is this a function? NO, use the vertical line test.

  20. Another way is called a: Function Table: input (x) ⟹ the function rule ⟹ output (y) What is the rule of this function?_________________________________

  21. Function Table: input (x) ⟹ the function rule ⟹ output (y) What is the rule of this function? -3x - 5

  22. Function Table: input (x) ⟹ the function rule ⟹ output (y) What is the rule of this function? -3x - 5 What is happening to x?________________________________________

  23. Function Table: input (x) ⟹ the function rule ⟹ output (y) What is the rule of this function? -3x - 5 What is happening to x? x is being multiplied by -3, then combined with -5

  24. Function Table: input (x) ⟹ the function rule ⟹ output (y) What is the rule of this function? -3x - 5 What is happening to x? x is being multiplied by -3, then combined with -5 How could you write this rule as an equation?______________________

  25. Function Table: input (x) ⟹ the function rule ⟹ output (y) What is the rule of this function? -3x - 5 What is happening to x? x is being multiplied by -3, then combined with -5 How could you write this rule as an equation? y = -3x - 5

  26. Function Table: input (x) ⟹ the function rule ⟹ output (y) This Function Table represents the Function: y = -3x – 5 What is y, if x = - 4 ?

  27. Function Table: input (x) ⟹ the function rule ⟹ output (y) This Function Table represents the Function: y = -3x – 5 What is y, if x = - 4 ? y = 7

  28. Is this a function? y = 4x + 1 Yes, it’s linear, so think about the shape of the graph and the vertical line test! You can also plug values in for x and see what you get for y.