1. FUNCTION
DEFINITION:
A RELATION IN WHICH EACH ELEMENT OF THE DOMAIN IS PAIRED WITH EXACTLY ONE ELEMENT OF THE RANGE.
IN OUR OWN WORDS THIS MEANS ALL X-VALUES MUST BE DIFFERENT.
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2. HOW TO TELL IF A RELATION IS A FUNCTION:
IF THE RELATION IS GIVEN AS A SET OF ORDERED PAIRS, LOOK TO SEE IF ALL THE X-VALUES ARE DIFFERENT. IF THEY ARE DIFFERENT IT IS A FUNCTION, IF THEY ARE NOT ALL DIFFERENT IT IS NOT A FUNCTION.
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3. EXAMPLE: FUNCTION- {(3, 2), (4, 5), (-2, 2)}
BECAUSE ALL X-VALUES ARE DIFFERENT.
NOT A FUNCTION- {(3, 4), (2, 3), (3, -3)} BECAUSE 3 IS THE X-VALUE IN THE FIRST AND 3RD ORDERED PAIR.
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4. HOW TO TELL IF A RELATION IS A FUNCTION:
IF THE RELATION IS GIVEN AS A TABLE ALL X-VALUES MUST BE DIFFERENT.
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5. EXAMPLE
FUNCTION: X Y 3 2 -4 5 6 -1
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6. EXAMPLE:
NOT A FUNCTION X Y 3 2 4 9 5
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7. HOW TO TELL IF A MAPPING IS A FUNCTION:
FUNCTION – EACH X-VALUE CAN ONLY HAVE ONE LINE DRAWN FROM IT.
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8. MAPPING THAT IS A FUNCTION
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9. MAPPING THAT IS NOT A FUNCTION:
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10. HOW TO DETERMINE IF A GRAPH IS A FUNCTION
VERTICAL LINE TEST: IF NO VERTICAL LINE CAN BE DRAWN SO THAT IT INTERSECTS THE GRAPH MORE THAN ONCE, THEN THE GRAPH IS A FUNCTION.
ALSO KNOWN AS THE PENCIL TEST
VERTICAL LINE IS A LINE THAT GOES UP AND DOWN
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11. EXAMPLES OF VERTICAL LINE TEST
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12. EXAMPLES OF VERTICAL LINE TEST
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13. EXAMPLES OF VERTICAL LINE TEST
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14. EXAMPLES OF VERTICAL LINE TEST
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15. EXAMPLES OF VERTICAL LINE TEST
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16. EXAMPLES OF VERTICAL LINE TEST
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17. HOW TO DETERMINE IF AN EQUATION IS A FUNCTION
SOLVE FOR Y
GRAPH THE EQUATION ON THE CALCULATOR
DO THE VERTICAL LINE TEST
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18. 1. x + y = 3
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19. 2. y = -3x + 4
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20. 3. x = 5
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21. 4. y = x2 – 2x +3
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22. 5. -3x - 2y = -6
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23. FUNCTION NOTATION
FUNCTION NOTATION: EQUATIONS THAT ARE FUNCTIONS CAN BE WRITTEN 2 WAYS
1. EQUATION Y = 3X + 4
2. FUNCTION f(x) = 3X + 4
f(x) MEANS THE SAME AS Y.
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24. TO FIND FUNCTION VALUES:
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