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**Objectives The student will be able to:**

1. To determine if a relation is a function. 2. To find the value of a function. Designed by Skip Tyler, Varina High School Modified by Johnny Kissko, Frenship High School

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Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). f(x) y x

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Function Notation Input Name of Function Output

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**Determine whether each relation is a function.**

1. {(2, 3), (3, 0), (5, 2), (4, 3)} YES, every domain is different! f(x) 2 3 f(x) 3 f(x) 5 2 f(x) 4 3

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**Determine whether the relation is a function.**

2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)} f(x) 4 1 f(x) 5 2 NO, 5 is paired with 2 numbers! f(x) 5 3 f(x) 6 f(x) 1 9

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**Is this relation a function? {(1,3), (2,3), (3,3)}**

Yes No Answer Now

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**Vertical Line Test (pencil test)**

If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! FUNCTION! NOPE!

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Vertical Line Test FUNCTION! NO! NO WAY! FUNCTION!

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**Is this a graph of a function?**

Yes No Answer Now

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**3(3)-2 3 7 -2 -8 3(-2)-2 Given f(x) = 3x - 2, find: 1) f(3) = 7**

= -8 3(-2)-2 -2 -8

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**Given h(z) = z2 - 4z + 9, find h(-3)**

(-3)2-4(-3)+9 -3 30 h(-3) = 30

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Given g(x) = x2 – 2, find g(4) 2 6 14 18 Answer Now

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**Given f(x) = 2x + 1, find -4[f(3) – f(1)]**

-40 -16 -8 4 Answer Now

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2.1 Relations and Functions A relation is a set of pairs of input and output values. – There are four different ways to represent relations.

2.1 Relations and Functions A relation is a set of pairs of input and output values. – There are four different ways to represent relations.

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