2.3 – Functions and Function

Notation

Objectives:

1. TSW identify whether an equation is a function.

2. TSW evaluate functions using function notation.

Definitions

Relation – a set of ordered pairs

Function – a relation in which, for each distinct value of the first component (x) of the ordered pairs, there is EXACTLY ONE value of the second component (y)

For a function, the x values can’t repeat.

Independent variable – x values

Dependent variable – y values

Domain – x values (input)

Range – y values (output)

Example 1

Decide whether the relation is a function.

M is a function because each x-value has one

y-value. X values do not repeat!

Example 2

Function?

P is not a function because the x-value –4 has two y-

values.

Example 3

Give the domain and range. Is the relation a

function?{(–4, –2), (–1, 0), (1, 2), (3, 5)}

Domain(x): {–4, –1, 1, 3}

Range(y): {–2, 0, 2, 5}

Function?

Example 4

•Function?

•Domain?

•Range?

Example 5

•Function?

•Domain?

•Range?

Example 6

Function?

Domain?

Range?

2yx =

Function Notation “f(x)” read as

“f of x.”

== y as same theis )(xf

92xy .7 +=

Write in function notation:

1-9xxy .8 2+=

Example 9

Let and .

Find:

f(–3)=

f(r)=

g(r + 2)=

Example 10

Find f(–1) for each function.

f(x) = 2x2 – 9

f = {(–4, 0), (–1, 6), (0, 8), (2, –2)}

Example 11

Determine the intervals over

which the function is

increasing, decreasing, or

constant. (use x values

only!)

decreasing

constant

increasing

Homework

2.3 page 213 #’s 1-21 E.O.O, 41-53 E.O.O.,

59-63 odd, 73, 75

E.O.O – every other odd so 1,5,9,13,17,21 and

41,45,49,53