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. Lesson 47

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. Lesson 47

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. Lesson 47

HOW TO TELL IF A RELATION IS A FUNCTION: IF THE RELATION IS GIVEN AS A TABLE ALL X-VALUES MUST BE DIFFERENT. Lesson 47

EXAMPLE FUNCTION: X Y 3 2 -4 5 6 -1 Lesson 47

EXAMPLE: NOT A FUNCTION X Y 3 2 4 9 5 Lesson 47

HOW TO TELL IF A MAPPING IS A FUNCTION: FUNCTION – EACH X-VALUE CAN ONLY HAVE ONE LINE DRAWN FROM IT. Lesson 47

MAPPING THAT IS A FUNCTION Lesson 47

MAPPING THAT IS NOT A FUNCTION: Lesson 47

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 Lesson 47

EXAMPLES OF VERTICAL LINE TEST Lesson 47

EXAMPLES OF VERTICAL LINE TEST Lesson 47

EXAMPLES OF VERTICAL LINE TEST Lesson 47

EXAMPLES OF VERTICAL LINE TEST Lesson 47

EXAMPLES OF VERTICAL LINE TEST Lesson 47

EXAMPLES OF VERTICAL LINE TEST Lesson 47

HOW TO DETERMINE IF AN EQUATION IS A FUNCTION SOLVE FOR Y GRAPH THE EQUATION ON THE CALCULATOR DO THE VERTICAL LINE TEST Lesson 47

1. x + y = 3 Lesson 47

2. y = -3x + 4 Lesson 47

3. x = 5 Lesson 47

4. y = x2 – 2x +3 Lesson 47

5. -3x - 2y = -6 Lesson 47

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. Lesson 47

TO FIND FUNCTION VALUES:   Lesson 47