Download Linear and Non-Linear Relationships

Linear and Non-Linear
Relationships
How would you like to get Paid?
• Chose one option calculate for one
month/30 days
• Option A ~ $100 a day
• Option B ~ $0.01 for the first day, then
double the amount for each day you work
until the end of the month.
• Option C ~ The Square of the number of
days you worked. Example on day five you
would get $25.
Each option represents a type of
relation
• Option A is a linear relation
• Option B is an Exponential relation
• Option C is a Quadratic relation
Linear Relation
• A relation between two variables that
appears in a straight line when graphed
y = 2x + 1 is a linear relation
Almost all linear relations take this form.
Graph of a linear relationship
A: (-2.01, -1.01)
C
B: (0.00, 1.00)
C: (2.01, 2.99)
2
B
-5
5
A
-2
Exponential Relation
• A relation between two variables where
one of the variables is an exponent
• Example
• a= 4b
• is an exponential relation
Example of an exponential relation
fx = 4x
C: (1.00, 3.99)
4
A: (0.00, 1.00)
C
B: (-2.99, 0.00)
2
A
-5
B
5
-2
-4
Quadratic relations
• A relation between two variables that
appears as a parabola when graphed
• y = -x2 + 8
• Is a quadratic relation
• A parabola is a U shaped curve
Quadratic relation
8
L
6
fx = -x2+8
I: (2.82, 0.03)
4
J: (-2.83, 0.01)
K
K: (-2.00, 3.98)
M
L: (0.00, 8.00)
M: (2.01, 3.97)
2
-5
I
J
-2
-4
-6
5
Comparing table of values
•
y = 2x
y = 2x
y = x2
x
y
x
y
x
y
-2
-4
-2
¼
-2
4
-1
-2
-1
½
-1
1
0
0
0
1
0
0
1
2
1
2
1
1
2
4
2
4
2
4
Geometers Sketch pad
• Geo Sketch pad demo given in class of
three relations
Comparing table of values
x
y
x
y
x
y
-2
-4
-2
¼
-2
4
-1
-2
-1
½
-1
1
0
0
0
1
0
0
1
2
1
2
1
1
2
4
2
4
2
4
Differences
• When examining tables you are to look at
the differences in the x and y values.
• If the first difference of the x and y value is
increasing by a constant amount the
relation is linear
• If the first difference of x is constant and y
is increasing by repeated multiplication the
relation is exponential
• If there is no set pattern for the y values
we then check the second difference in the
table. If the second difference is increasing
by a set amount we can say that the
relationship is Quadratic.
• If there is no set pattern in the second
difference the relation cannot be identified
as any of our three choices.
Practice 2
x
y
x
y
x
y
-2
-5
-2
1/9
-2
9
-1
-2
-1
1/3
-1
3
0
1
0
1
0
0
1
4
1
3
1
3
2
9
2
7
2
9