IDENTIFYING FUNCTIONS
Focus 11 - Learning Goal: Students will be able to construct,
compare and analyze function models and interpret and
solve contextual problems.
4
In addition to level
3.0 and above and
beyond what was
taught in class, the
student may:
- Make connection
with other concepts
in math.
- Make connection
with other content
areas.
3
Students will be able to
construct, compare, and
analyze function models and
interpret and solve contextual
problems.
Function models:
- absolute value
- square root
- cube root
- piecewise
Analyze multiple
representations of functions
using:
- Key features
- Translations
- Parameters/limits of domain
2
Students will be able
to construct and
compare function
models and solve
contextual problems.
Function models:
- linear
- exponential
- quadratic
Illustrate the
graphical effects of
translations on
function models
using technology.
1
With help from the
teacher, the
student has partial
success with the
unit content.
0
Even with help,
the student has
no success with
the unit content.
Look for the patterns you observe when
examining the parent functions in the tables.
Can you determine their family?
Table A
Table B
x
-2
-1
0
1
2
3
x
-2
-1
0
1
2
3
y
-9
-4
1
6
11
16
y
6
3
0
3
6
9
Table C
x
-2
-1
0
1
2
3
y
Err
Err
0
1
1.41
1.73
Is one of them absolute value, linear, exponential, square root, cube root, or
quadratic?
How could you tell Table A was linear?
How could you tell Table B was quadratic?
How could you tell Table C was a square root function?
If you can determine a pattern, use the following
tip: (this only works if the x-values are consecutive.)
First Differences
(subtract successive y-values)
Equal ?
Yes. Linear
x
-1
0
1
2
3
y
4
1
-2
-5
-8
-3
-3
-3
-3
This is a linear function.
If you can determine a pattern, use the following
tip: (this only works if the x-values are consecutive.)
First Differences
(subtract successive y-values)
Equal ?
Yes. Linear
No. Calculate second differences.
(Subtract differences between
successive first differences.)
Equal?
Yes.
Quadratic
No.
If the ratios are equal,
Exponential
x
-8
-7
-6
-5
-4
y
576
441
324
225
144
-135
-117
-99
-81
+18
+18
+18
This is a quadratic function.
If you can determine a pattern, use the following
tip: (this only works if the x-values are consecutive.)
First Differences
(subtract successive y-values)
Equal ?
Yes. Linear
No. Calculate second differences.
(Subtract differences between
successive first differences.)
Equal?
Yes.
Quadratic
No.
If the ratios are equal,
Exponential
x
-1
0
1
2
3
y
-1
-3
-9
-27
-81
-2
-6
-18
-54
-4
-12
-36
•3
•3
The
ratios
are
equal.
This is an exponential function.
Given the table of values, identify the type of
function: linear, quadratic, or exponential?
Table D
x
y
-9 162
-8
-7
-7
-5
128
98
72
50
-34
-30
-26
-22
Quadratic Function
-4
-4
-4
Table E
x
y
-8 25
-7 23
-6
-5
-4
21
19
17
Linear Function
-2
-2
-2
-2
Table F
x
y
-2
0.18
-1
0.54
0
1.62
1
4.86
2
14.58
0.36
1.08
3.24
0.72
2.16
6.48
9.72
Exponential Function
•3
•3
Find the missing values in the table:
Table G
x
y
-2
2
-1 -3
0
1
2
-8
-13
-18
 What should you do 1st?
 Next, determine what type of function it is.
 Lastly, calculate the missing value.
Find the missing values in the tables:
Table H
x
y
-2
1
-1
0
1
2
2
4
8
16
Exponential
Table J
x
y
2
-36
3
4
5
6
-81
-144
-225
-324
Quadratic