Name
Hour
Function Families Poster Activity
After Course 2 Unit 6 Lesson 3
You have studied various patterns of change and how those patterns could be modeled
using constant, linear, exponential, power, absolute value, square root, step,
logarithmic, and sine functions. It is helpful to thing about each “family” of functions in
terms of basic symbolic rules and their corresponding graphs.
In this activity, you will create examples of each of the basic types of functions.
1. Create a sample table and graph of each example given.
2. Explain how the table and graph patterns can be predicted from the equation.
3. For each function family, describe how the different parameters impact the graph
and the table patterns.
Each group will create a poster for one of the families of functions that includes all of the
information.
Function
Family/Example
Table
Graph
Constant functions
y=a
y=4
x
-3
-2
-1
0
1
2
3
How does a affect the table/graph?
y
Name
Function
Family/Example
Hour
Table
Graph
Linear functions
y = a + bx
y = -3 + 0.5x
x
-3
y
-2
-1
0
1
2
3
x
-3
y = 4 – 2x
-2
-1
0
1
2
3
How does a affect the table/graph?
How does b affect the table/graph?
y
Name
Function
Family/Example
Exponential
Functions:
Exponential Growth
Hour
Table
x
-3
y = a (b x) where b > 1
-2
y = 0.5 (2 x)
-1
Graph
y
0
1
2
3
Exponential
Functions:
Exponential Decay
y = a (b x) where
0<b<1
y = 3 (0.5 x)
x
-3
y
-2
-1
0
1
2
3
Referring to both exponential functions above:

How does a affect the table/graph?

How does b affect the table/graph?
Name
Function
Family/Example
Hour
Table
Graph
Power Functions:
Quadratic Model
y = ax 2
y = 2x2
x
-3
y
-2
-1
0
1
2
3
Power Functions:
Cubic Model
y = ax 3
y = 2x3
x
-3
y
-2
-1
0
1
2
3
Referring to both power models above:

How does a affect the table/graph?
Name
Function
Family/Example
Power Functions:
Inverse Model
y=
y=
Hour
Table
x
-3
a
x
-2
5
x
0
Graph
y
-1
1
2
3
Power Functions:
Inverse Squared
y=
y=
x
-3
a
x2
-2
4
x2
0
y
-1
1
2
3
Referring to both inverse power models above:

How does a affect the table/graph?

How does squaring the denominator affect the table/graph?
Name
Function
Family/Example
Absolute Value
Function:
Hour
Table
x
-3
y = a |x|
-2
y = 2 |x|
-1
Graph
y
0
1
2
3
y = -3 |x|
x
-3
y
-2
-1
0
1
2
3
Referring to both absolute value models above:

How does a affect the table/graph?
Name
Function
Family/Example
Square Root
Function:
y = a √x
y = √x
Hour
Table
x
-4
Graph
y
-3
-2
-1
0
1
2
3
4
y = -2 √x
x
-4
y
-3
-2
-1
0
1
2
3
4
Referring to the square root functions above:

How does a affect the table/graph?
Name
Function
Family/Example
Hour
Table
Graph
Step Function:
x
-3
y
-2
-1
0
1
2
3
Referring to the step functions above:

How are step functions different from all of the other functions?
Name
Function
Family/Example
Logarithmic
Function:
y = log x
Hour
Table
x
-3
Graph
y
-2
-1
0
1
2
3
Exponential
Function:
y = 10x
x
-3
y
-2
-1
0
1
2
3
Referring to the functions above:

How are the logarithmic and exponential functions related to each other? How are
they similar/different?
Name
Function
Family/Example
Hour
Table
Graph
Sine Function:
y = AsinBx + C
y = 3 sin 2x
x
0
y
45
90
135
180
226
270
315
360
y = 4 sin x + 1
x
0
y
45
90
135
180
226
270
315
360
Referring to the trigonometric functions above:

How does A affect the table/graph?

How does B affect the table/graph?

How does C affect the table/graph?