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# Functions and graphs

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### Functions and graphs

1. 1. (A) (B) (C) ° 32 mpg ° 8 mpg ° 16 mpg
2. 2.  The values that make up the set of independent values are the domain The values that make up the set of dependent values are the range. State the domain and range from the 4 examples of relations given.
3. 3.  Transitive: If a = b and b = c then a = c Identity: a + 0 = a, a • 1 = a Commutative: a + b = b + a, a • b = b • a Associative: (a + b) + c = a + (b + c) (a • b) • c = a • (b • c) Distributive: a(b + c) = ab + ac a(b - c) = ab - ac
4. 4. if a is positiveif a is negative
5. 5.  A Relation maps a value from the domain to the range. A Relation is a set of ordered pairs. The most common types of relations in algebra map subsets of real numbers to other subsets of real numbers.
6. 6. Domain Range This is often referred to as a diagrammatic representation of a 3 π relation. Note that each element in the domain is 11 -2 connect to it’s respective range1.618 2.718 element by the arrow.
7. 7.  The relation is the year and the cost of a first class stamp. The relation is the weight of an animal and the beats per minute of it’s heart. The relation is the time of the day and the intensity of the sun light. The relation is a number and it’s square.
8. 8.  If a relation has the additional characteristic that each element of the domain is mapped to one and only one element of the range then we call the relation a Function.
9. 9. FUNCTION CONCEPT f x yDOMAIN RANGE
10. 10. NOT A FUNCTION R x y1 y2DOMAIN RANGE
11. 11. FUNCTION CONCEPT f x1 y x2DOMAIN RANGE
12. 12.  Symbolic • Graphical{x )y=2 } ( ,y x or y=2 x• Numeric X Y 1 2 5 10 • Verbal The cost is twice -1 -2 the original 3 6 amount.
13. 13.  A truly excellent notation. It is concise and useful. = () y fx
14. 14. = () y fx Name of the function• Output Value • Input Value• Member of the Range • Member of the Domain• Dependent Variable • Independent VariableThese are all equivalent These are all equivalentnames for the y. names for the x.
15. 15.  The f notation f( ) x 1 x= + f( ) () 1 2 = 2+