IDENTIFYING FUNCTIONS

4 3 2 1 0In 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.  

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

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.

With help from the teacher, the student has partial success with the unit content.

Even with help, the student has no success with the unit content.

Focus 11 - Learning Goal: Students will be able to construct, compare and analyze function models and interpret and solve contextual problems.

Look for the patterns you observe when examining the parent functions in the tables. Can you determine their family?

x -2 -1 0 1 2 3

y -9 -4 1 6 11 16

Table A x -2 -1 0 1 2 3

y 6 3 0 3 6 9

Table B

x -2 -1 0 1 2 3

y Err Err 0 1 1.41

1.73

Table C

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.)

x y

-1 4

0 1

1 -2

2 -5

3 -8

First Differences(subtract successive y-values)Equal ? Yes. Linear

-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.)

x y

-8 576

-7 441

-6 324

-5 225

-4 144

First Differences(subtract successive y-values)Equal ? Yes. Linear

No. Calculate second differences.

(Subtract differences between successive first differences.)

Equal?

Yes. No.Quadratic If the ratios are equal, Exponential

-135

-117-99

-81

This is a quadratic function.

+18+18

+18

If you can determine a pattern, use the following tip: (this only works if the x-values are consecutive.)

x y

-1 -1

0 -3

1 -9

2 -27

3 -81

First Differences(subtract successive y-values)Equal ? Yes. Linear

No. Calculate second differences.

(Subtract differences between successive first differences.)

Equal?

Yes. No.Quadratic If the ratios are equal, Exponential

-2

-6-18

-54

This is an exponential function.

-4

-12

-36

• 3

• 3

The ratios are equal

.

Given the table of values, identify the type of function: linear, quadratic, or exponential?

x y

-9 162

-8 128

-7 98

-7 72

-5 50

Table D x y

-8 25

-7 23

-6 21

-5 19

-4 17

Table E x y

-2 0.18

-1 0.54

0 1.62

1 4.86

2 14.58

Table F

-34

-30

-22

-26

-4

-4

-4

Quadratic Function

-2

-2

-2

-2

Linear Function

0.361.08

9.72

3.24

0.722.166.48

• 3

• 3

Exponential Function

Find the missing values in the table:

What should you do 1st?Next, determine what type of function it is.Lastly, calculate the missing value.

x y

-2 2

-3

0

1 -13

2 -18

Table G

-1 -

8

Find the missing values in the tables:

x y

-2 1

-1 2

0

1 8

16

Table H x y

2 -36

3 -81

4 -144

5

6 -324

Table J

2

4

-225

Exponential Quadratic