Drill #61

For each equation make an x,y chart and find 3 points for each equation. Plot each set of points on a coordinate plane.

1. x + y = 10

2. 3x – y = 6

3. y = 2x – 2

5-5 Functions

Objective: To determine whether a given relation is a function, and to find the value of a function for a given element in the domain.

OPEN BOOKS TO PAGE 287.

(18.) Function

Definition: A function is a relation in which each element of the domain (x) is paired with exactly one element of the range (y).

For every input (x) there is exactly one output, f(x) or y. Think of a function as a machine that transforms a number (domain) into another number (range).

• Examples: Non-Examples:y = 10 x = 10 |x| = y x = |y| x + y = 6 2yx

Functions

{(1,0), (2,0), (3,0)}

x y

2 3

1 -2

0

X Y

2 0

1 -2

0 3

Non Functions

{(1,0), (1,1), (1,2)}

x y

2 3

1 -2

0

X Y

1 0

1 -2

0 3

Find the function(Classwork #61)

• Determine whether each relation is a function:

4. {(2,3), (3,0), (5,2), (-1, -2), (4, 1)}

5.

x y 6.

3

4 0

-3 -6

-8 10

x y

4 -1

5 2

5 3

6 6

-1 1

(19.) Vertical Line Test

• If any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.

• To perform a vertical line test, use a pencil or a straight-edge and pass it vertically over your graph. If it touches any 2 points at the same time then the relation is not a function.

Study Guide 5-5

Do Study Guide 5-5

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(20.) Functional Notation

• Equations that are functions can be written in the form called functional notation.

• In functional notation y is replaced with f(x) (‘f’ of ‘x’).• In functional notation x represents the elements in the

domain and f(x) represents elements in the range.• Ordered pairs for functions are (x, f(x)).

• Example: Functional Notation:y = 3x – 7 f(x) = 3x – 7

f(1) = 3(1) – 7 = -4 f(2) = 3(2) – 7 = -1

Examples

If h(x) = 3x + 2 find:

h(-4)

h(2)

h(w)

h(x – 6)

Classwork #73

If h(x) = 3x + 2 find:

4. h(-4) = 3(-4) + 2 = -105. h(2) = 3(2) + 2 = 86. h(w) = 3(w) + 2 = 3w + 27. h(x – 6) = 3 (x – 6) + 2

= 3x – 18 + 2 = 3x – 16

The Celsius Function

• The function for converting Celsius to Fahrenheit is:

• Find F(0), F(10), F(20), F(30)

325

9)( xxF

Fahrenheit to Celsius

Domain

(x)

F(x) Range

F(x) or y

0 F(0)=9/5(0)+32 32

10 F(10)=9/5(10)+32 50

20 F(20)=9/5(20)+32 68

30 F(30)=9/5(30)+32 86

5-5 Practice

• 5-5 Study Guide

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