Download Functions Patterns and Proportional Relationships

Functions, Patterns and
Proportional Relationships
Direct and Indirect Proportions
Function
A function is like a machine
 It has an input (x-value) and an
output (y-value)
 For every input, there is exactly
ONE output
 A function can be displayed by a
rule, a table or graph.
Function Introduction Video

Function 1
y=5x - 1
Input
Rule
Output
x
5x – 1
y
-2
0
3
6
Function 2
y=-2x2
Input
Rule
Output
x
-2x2
y
-2
2
3
4
Can you find the pattern?
Input (x)
Output (y)
1
4
2
6
3
8
4
5
6
1. Complete the table
2. Can you write the function?
Graph the Function
Y=x÷4
Input
Rule
Output
Ordered Pair
X
X÷4
Y
(x,y)
-4
0
2
4
Describing Functions
X
1
2
3
4
y
9
18
27
36
“As x increases by 1, y increases by _____”
Direct Proportion


Any function that can be
written in the form y=kx,
where K is a constant
EXAMPLE: y= 9x
When one
number
increases,
the other
number
also
increases
X
1
2
3
4
y
9
18
27
36
Direct Proportion Example

David earns $15 each hour he
works for his grandmother doing
odd jobs around the house.
X (hours
worked)
Y ($
made)
1
2
3
4
Direct Proportion Example
X (hours
worked)
1
2
3
4
Y ($
made)
$15
$30
$45
$60
Let x stand for the number of hours David worked and
let y stand for the number of dollars she earns:
Y= ___ ___
Direct Proportion

Y= 15x
A direct proportion exists!
$$ made

Hours worked
Direct Proportions in graphs


To determine whether a line is the
graph of a direct proportion, follow
this rule:
If a straight-line graph passes
through the point (0,0), it is the
graph of a direct proportion
Which line is the direct proportion?
n
m
Indirect Proportion


When two numbers are multiplied
and the answer is a constant (k)
EXAMPLE: xy=k
y= k
x
For (1,8), xy = ______
For (2,4), xy = ______
For (4,2), xy = ______
For (8,1), xy = ______
Indirect Proportion
Thinking it Through
 Is
the function y=3x + 3
a direct proportion?
Thinking it Through

Is the function y=3x + 3 a direct
proportion?
Step 1: Pick a point
If x = 1, y = ________
Y=
X
_______
Thinking it Through

Is the function y=3x + 3 a direct
proportion?
Step 3: Pick another point
If x=3, y= ___________
Y=
X
_______
Thinking it Through

Is the function y=3x + 3 a direct
proportion?
Another Way:
Direct Proportions must pass through (0,0)
SO…when x=0, does y=0???
Hints for Proportion Questions

Numbers being multiplied??
It’s a Direct Proportion!

Numbers being divided??
It’s an Indirect Proportion!
Hints for Proportions

Graph a straight line, going through
(0,0)??
It’s a Direct Proportion!

Graph a curve??
It’s an Indirect Proportion!
Question 1

Which describes the equation
y = 50/x ?
Direct proportion
b. Indirect proportion
C. Neither
a.
Question 2

a.
b.
c.
Which statement describes the
equation y = 10x ?
Direct proportion
Indirect proportion
Neither
Question 3

The Willy Wonka Factory can make
2,000 chocolate bars per hour. This
means there is a direct proportion
between the number of hours the
factory is operating and
_____________________________
____________________________.
 COACH
 Pg.154
 Pg.158
 Pg.162