Intro to Functions College Algebra

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

Function Notation Input Name of Function Output

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

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

Is this relation a function? {(1,3), (2,3), (3,3)} Yes No Answer Now

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!

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

Is this a graph of a function? Yes No Answer Now

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

Given h(z) = z2 - 4z + 9, find h(-3) (-3)2-4(-3)+9 -3 30 9 + 12 + 9 h(-3) = 30

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

Given f(x) = 2x + 1, find -4[f(3) – f(1)] -40 -16 -8 4 Answer Now

Lets look at some function Type questions ( x ) = 2 + 4 a n d g 1 - F i 3 If = 8 2 2 3 = -8 3

x y 5 6 7 Relations and functions can be shown many different ways. Are these relations or functions? Function & Relation x y 1 2 3 4 x y 5 6 7 5 6 7 (1, 5), (2, 6), (3, 7), (4, 6)

Are these relations or functions? Not a Function but a Relation x y x y 5 6 1 7 1 6 1 2 5 6 7

Are these relations or functions? x y Not a function But a relation 5 6 8 11 1 2 3 x y 5 6 11 8

These all represent the SAME function! In words: Double the number and add 3 As an equation: y = 2x + 3 These all represent the SAME function! As a table of values: x y -2 -1 -1 1 0 3 1 5 As a set of ordered pairs: (-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)

Evaluate the Following Function in Function Notation f(x) = 2x – 3 when x = -2 f(-2) = 2(-2) – 3 = -4 – 3 = -7

You try! Evaluate the Following Function in Function Notation… f(x) = -7x – 3 when x = 4 f(4) = -7(4) – 3 = -28 – 3 = -31

Is the relation a function? If yes, state the domain and range. x y Yes, the relation is a function! 1 -2 2 -3 The domain is 1, 2, 3, and 4 3 -3 4 -5 The range is -2, -3, -3, -5

What values are excluded from the domain of each function? 1. 2. 3. 4. 4 -4 none