Dependent and Independent Variables

1
Dependent and Independent Variables
The Dependent Variable changes in response to
another variable.
Output Value
The Independent Variable determines the value of
the dependent variable.
Input Value
What would that look like as an equation?
Output Value
Dependent Variable
Input Value
Independent Variable
2
Representing a Geometric Relationship
The diagram below shows a relationship between
the number of rectangles and the perimeter of the
figure they form. Represent this relationship
using a table, words, an equation, and a graph.
Asi De Facil
Graph
22 18 14 10 6 2
Table
Words
Equation
Multiply the number of rectangles by 2 and add 12
to get the perimeter.
1 2 3 4
3
Representing a Linear Function
A function is a relationship that pairs each
input value with exactly one output value.
A linear function is a function whose graph is a
non-vertical line.
The accompanying table shows the relationship
between the number of photos, x, you take and the
amount of memory, y, left on your memory chip.
Is the relationship a linear function? Describe
the relationship using words, an equation, and a
graph.
Graph
This is a linear function because there is a
constant rate of change.
512 510 508 506 504 502 500
-3
Equation
That was easy
-3
-3
Words
The amount of memory left is 512 minus 3 times
the number of photos taken.
1 2 3 4
4
More Representing Linear Functions
For each table, determine whether the
relationship is a linear function. Then
represent the relationship using words, an
equation, and a graph.
Equation
Equation
Asi De Facil
5
-6
5
-6
Graph
Graph
5
-6
22 18 14 10 6 2
22 18 14 10 6 2
This is a linear function because there is a
constant change.
This is a linear function because there is a
constant change.
Words
Words
Start with 7 and add 5 for each increase of 1 to
x.
Start with 20 and subtract 6 for each increase of
1 to x.
1 2 3 4
1 2 3 4
5
Homework
Page 243 - 244 6 13 All Questions
6
Classifying Functions as Linear or Nonlinear
Determine whether each function is linear or
nonlinear.
Linear
Nonlinear
Linear
Nonlinear
Linear
Linear
Nonlinear
Nonlinear
7
More Classifying Functions
Graph the function shown by each table and tell
whether the function is linear or nonlinear.
11 9 7 5 3 1
11 9 7 5 3 1
6 4 2 0 -2 -4
11 9 7 5 3 1
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
Nonlinear
Nonlinear
Nonlinear
Linear
8
Writing a Rule to Represent a Nonlinear Function
Each set of ordered pairs represents a function.
Write a rule that represents each function.
That takes some work but I think I can do it.
9
Homework
Page 250 6 11 and 14, 15
10
Graph of a Function
Model each rule with a table and a graph
x y



x y



x y



-3
7
-2
10
-3
1
0
-2
0
8
0
4
3
-11
2
6
3
7
8 6 4 2 -2 -4 -6 -8
8 6 4 2 -2 -4 -6 -8
8 6 4 2 -2 -4 -6 -8
-8 -6 -4 -2 2 4 6 8
-8 -6 -4 -2 2 4 6 8
-8 -6 -4 -2 2 4 6 8
11
8 6 4 2 -2 -4 -6 -8
x y



-8 -6 -4 -2
2 4 6 8
12
Homework
Page 257 10 20 Even Numbers