Types of Functions
Recall (don’t write)
• Constant function:
• Example: You rent a movie ($5 for one day). What is the
relationship between the number of hours you keep the
video and the cost for the rental?
•
Time
0
5
10
15
…
x
(h)
Cost ($)
Recall (don’t write)
• Constant function:
• Example: You rent a movie ($5 for one day). What is the
relationship between the number of hours you keep the
video and the cost for the rental?
•
Time
0
5
10
15
…
x
(h)
Cost ($)
5
5
5
5
Recall (don’t write)
• Constant function:
• Example: You rent a movie ($5 for one day). What is the
relationship between the number of hours you keep the
video and the cost for the rental?
•
Time
0
5
10
15
…
x
(h)
Cost ($)
5
5
5
5
• Table of values: dependent value does not change
5
Recall (don’t write)
• Graph : Horizontal line
Cost to Rent a Video
Cost ($)
5
4
3
2
1
0
5
15
10
Time (h)
• Rule: y = b
(a constant value)
• In this example the rule is cost = $5
Recall (don’t write)
• Direct Variation
• Example: You have a “pay-as-you-go” cell phone. You pay $0.30
per minute
Recall (don’t write)
• Direct Variation
• Dependant variable changes by a constant amount (“a”)
• Values are proportional (you can cross multiply in the table of
values)
• Graph is an oblique line that passes through the origin (no start up
cost)
• Rule is y = ax
Partial Variation (new, write
these!)
• Example: You pay $30 a month for your cell phone, plus
$0.10 cents per minute you talk on the phone.
• ____________ depends on _____________
•
(Dependent)
(Independent)
• Table of values:
0
5
10
50
…
x
Partial Variation (new, write
these!)
• Example: You pay $30 a month for your cell phone, plus
$0.10 cents per minute you talk on the phone.
• __Cost_______ depends on # of minutes___
•
(Dependent)
(Independent)
• Table of values:
0
5
10
50
…
x
Partial Variation (new, write
these!)
• Example: You pay $30 a month for your cell phone, plus
$0.10 cents per minute you talk on the phone.
• ___Cost_____ depends on __# of minutes__
•
(Dependent)
(Independent)
• Table of values:
Time
(min)
Cost ($)
0
5
10
50
…
x
Partial Variation (new, write
these!)
• Example: You pay $30 a month for your cell phone, plus
$0.10 cents per minute you talk on the phone.
• ___Cost_____ depends on _# of minutes____
•
(Dependent)
(Independent)
• Table of values:
Time
(min)
0
5
10
50
Cost ($)
30
30.50
31.00
35.00
…
x
Partial Variation (new, write
these!)
• Example: You pay $30 a month for your cell phone, plus
$0.10 cents per minute you talk on the phone.
• ___Cost_____ depends on _# of minutes__
•
(Dependent)
(Independent)
• Table of values:
Time
(min)
0
5
10
50
Cost ($)
30
30.50
31.00
35.00
…
x
0.1x + 30
Cell Phone Costs
Cost ($) 34
• Graph
33
32
31
30
29
28
0
10
30
20
Time
(min)
• Rule:
• Cost = 0.1 per min and 30 fee
• Cost = 0.1x + 30
• Partial : y = ax + b
• “a” is the slope
• “b” is the start up cost
Rules for Straight Lines
Start with y = ax + b
a = slope
b = initial
value
Constant
a=0
y=b
Direct
Partial
Rules for Straight Lines
Start with y = ax + b
a = slope
b = initial
value
Constant
a=0
y=b
Direct
Partial
Rules for Straight Lines
Start with y = ax + b
a = slope
b = initial
value
Constant
Direct
a=0
 y =b
b = 0 (no start up fee)
 y = ax
Partial
Rules for Straight Lines
Start with y = ax + b
a = slope
b = initial
value
Constant
Direct
Partial
a=0
 y =b
b = 0 (no start up fee)
 y = ax
y = ax + b
Rules for Straight Lines
Start with y = ax + b
a = slope
b = initial
value
Constant
Direct
Partial
a=0
 y =b
b = 0 (no start up fee)
 y = ax
y = ax + b