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1.4 Relations & Functions

1.4 Relations & Functions. Relation : a set of ordered pairs Domain (D): set of first coordinates of the pairs Range (R): set of second coordinates of the pairs Correspondence between domain & range is mapping Special mapping is a function !. (usually x-value). (usually y-value).

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1.4 Relations & Functions

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  1. 1.4 Relations & Functions

  2. Relation: a set of ordered pairs Domain (D): set of first coordinates of the pairs Range (R): set of second coordinates of the pairs Correspondence between domain & range is mapping Special mapping is a function! (usually x-value) (usually y-value)

  3. Function: f ; a relation in which each element in the domain is mapped to exactly one element in the range •  can we put this in our own words??... • Relations & functions can be expressed in different ways •  one popular one: f (x) • such as f (x)= 2x2 + 7 • *remember to evaluate f (x) for a particular value of x, • simply replace the value for x every time you see an x or g(x) = cosx

  4. a) b) c) Ex 1) Given , evaluate: *this one is something special…but we don’t want to spill the secret quite yet! 

  5. Remember – No dividing by 0 – No taking even roots of neg. #s If a function has no domain specified, it is “All Real #s” (R) You have to find domain? Ex 2) Find Domain & Range (confirm with graph) a) b) Graph on Calculator so…x≠ 0 Graph on Calculator so…x< 5

  6. Two functions are equal if the domain of f is equal to domain of g AND for all x in domain, f (x) = g(x) Ex 3) Are these functions equal? NO…. Domains are same but… h(x) ≠ m(x)

  7. Determining if a relation / rule / mapping is a function… Vertical Line Test!! all vertical lines drawn only touch graph 1 time – then YES! Ex 4) Are these functions? a) one-to-one function? passes horizontal line test c) b) y = 5 N/A (not a function) YES! NO! YES! NO! (basically, no y’s repeat)

  8. Homework #104 Pg 29 #1-23 odd, 24-27, 28, 35, 37, 38, 43, 44, 45, 49, 53, 55, 57

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