ALGEBRA IFunction Family Tree Project

Your task is to build a Function Family Tree. This will test your knowledge of the types of Transformations applied to Parent Functions.

You will start with a Parent Function who will have two children, Child A and Child B. Each child will have one different transformation applied to it. You will need to identify each transformation and graph the new function.

The two “children functions” you just graphed will each meet a function they fancy and get married, Spouse A and Spouse B. Each spouse will have one different transformation applied to it. You will need to identify the transformations and graph the functions of each of their spouses.

The two new happy couples will each have two children of their own, called Grandchildren. You will need to combine the equations of their parents, identify the functions, and graph the new functions for the first child. Then, you will perform the opposite transformations on the second child. So, the first child will be a combination of the transformations of the parents, and the second child will be the opposite of the transformations of the parents.

These 2 families will each adopt a child. You will need to identify each transformation and graph the new function of the adopted child. The adopted should come from a different “family.”

**Your graphs must be accurate. Once you find the equations of the functions you need to graph, plug them into the calculator and use the table of values to build your graphs.**

FUNCTION FAMILY TREE RUBRIC

ALGEBRA I

Una

ccep

tabl

e1

Stud

ent

iden

tifie

s m

ore

than

six

trans

form

atio

ns

inco

rrec

tly o

r is

mis

sing

mor

e th

an

six

iden

tific

atio

ns.

Stud

ent

iden

tifie

s m

ore

than

six

func

tion

rule

s in

corr

ectly

or i

s m

issi

ng m

ore

than

si

x fu

nctio

n ru

les.

Post

er is

insu

ffic

ient

or

not

han

ded

in.

Stud

ent i

s mis

sing

m

ore

than

four

gr

aphs

, inc

ompl

ete,

or

all

grap

hs a

re

grap

hed

inco

rrec

tly.

Uns

atis

fact

ory

2

Stud

ent i

dent

ifies

fiv

e to

six

trans

form

atio

ns

inco

rrec

tly, o

r is

mis

sing

five

to si

x id

entif

icat

ions

.

Stud

ent i

dent

ifies

fiv

e to

six

func

tion

rule

s inc

orre

ctly

, or

is m

issi

ng fi

ve to

six

func

tion

rule

s.

Post

er is

inco

mpl

ete

or is

mis

sing

in

form

atio

n.

Stud

ent i

s mis

sing

th

ree

to fo

ur g

raph

s, or

mos

t gra

phs a

re

inco

rrec

t.

Satis

fact

ory

3

Stud

ent i

dent

ifies

th

ree

to fo

ur

trans

form

atio

ns

inco

rrec

tly o

r is

mis

sing

thre

e to

four

id

entif

icat

ions

.

Stud

ent i

dent

ifies

th

ree

to fo

ur

func

tion

rule

s in

corr

ectly

or i

s m

issi

ng th

ree

to fo

ur

func

tion

rule

s.

Post

er is

com

plet

e an

d co

ntai

ns a

ll in

form

atio

n bu

t is

mes

sy o

r un

orga

nize

d.

Stud

ent i

s mis

sing

on

e or

two

grap

hs,

or s

ome

grap

hs a

re

inco

rrec

t.

Goo

d4

Stud

ent i

dent

ifies

on

e or

two

trans

form

atio

ns

inco

rrec

tly o

r is

mis

sing

one

or t

wo

iden

tific

atio

ns.

Stud

ent i

dent

ifies

on

e or

two

func

tion

rule

s inc

orre

ctly

or

is m

issi

ng o

ne o

r tw

o fu

nctio

n ru

les.

Post

er is

com

plet

e an

d co

ntai

ns a

ll in

form

atio

n ne

eded

. It

is b

asic

in d

esig

n.

Stud

ent g

raph

s all

func

tions

, but

doe

s no

t use

cor

rect

po

ints

. G

raph

s ar

e a

bit o

ff.

Out

stan

ding

5

Stud

ent i

s abl

e to

id

entif

y al

l tra

nsfo

rmat

ions

co

rrec

tly.

Stud

ent i

s abl

e to

id

entif

y al

l fun

ctio

n ru

les c

orre

ctly

.

Post

er is

com

plet

e an

d co

ntai

ns a

ll in

form

atio

n ne

eded

. It

is c

reat

ive

and

appe

alin

g to

the

eye.

Stud

ent i

s abl

e to

gr

aph

all f

unct

ions

ac

cura

tely

and

use

s co

rrec

t poi

nts.

Perf

orm

ance

In

dica

tors

Iden

tifyi

ng

Tran

sfor

mat

ions

Func

tion

Rul

es

Fam

ily T

ree

Post

er

Gra

phin

g Tr

ansf

orm

atio

ns

ALGEBRA IFunction Family Tree ChecklistDirections: Put a check next to each task you have completed.

Parent Function:Write down the function rule for the PARENT function.Name the type of function (Absolute Value, Quadratic, Linear, Square Root).Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.

Child Function A:Write down the function rule for CHILD FUNCTION A.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformation (Dilation, Reflection, Translation).

Child Function B:Write down the function rule for CHILD FUNCTION B.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformation (Dilation, Reflection, Translation).

Spouse Function A:Write down the function rule for SPOUSE FUNCTION A.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformation (Dilation, Reflection, Translation).

Spouse Function B:Write down the function rule for SPOUSE FUNCTION B.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformation (Dilation, Reflection, Translation).

Grandchild Function A1:

ALGEBRA ICreate a function rule that combines the function rules of Child A and Spouse A.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformations (Dilation, Reflection, Translation).

Grandchild Function A2:Create a function rule that combines the opposites of Child A and Spouse A.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformations (Dilation, Reflection, Translation).

Adopted Child Function A:Write down the function rule for ADOPTED CHILD FUNCTION A.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformations (Dilation, Reflection, Translation).

Grandchild Function B1:Create a function rule that combines the function rules of Child B and Spouse B.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformations (Dilation, Reflection, Translation).

Grandchild Function B2:Create a function rule that combines the opposites of Child B and Spouse B.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformations (Dilation, Reflection, Translation).

Adopted Child Function B:Write down the function rule for ADOPTED CHILD FUNCTION B.Graph the equation on your calculator.Mark the coordinates on the graph provided.Draw the function.Name the transformation (Dilation, Reflection, Translation).

ALGEBRA I

Parent Function

Type of Function: _____________________

Function Rule: ____________________

ALGEBRA I

Child Function A

Transformation: _____________________

Function Rule: ____________________

Child Function B

Transformation: _____________________

Function Rule: ____________________

ALGEBRA ISpouse Function A

Transformation: _____________________

Function Rule: ____________________

Spouse Function B

Transformation: _____________________

Function Rule: ____________________

ALGEBRA IGrandchild Function A1Transformation 1: _____________________Transformation 2: _____________________

Function Rule ______________________

Grandchild Function A2Transformation 1: _____________________Transformation 2: _____________________

Function Rule ______________________

Adopted Child Function ATransformation 1: _____________________Transformation 2: _____________________

Function Rule ______________________

ALGEBRA IGrandchild Function B1Transformation 1: _____________________Transformation 2: _____________________

Function Rule ______________________

Grandchild Function B2Transformation 1: _____________________Transformation 2: _____________________

Function Rule ______________________

Adopted Child Function BTransformation 1: _____________________Transformation 2: _____________________

Function Rule ______________________

ALGEBRA I

Project looks like this:

ALGEBRA IName________________________________________ Period ________ Date_____________________

Function Family Tree Writing Prompt

In at least 2 paragraphs (5 sentences each) answer the following questions. Make sure to be specific and detailed.

A) Describe how you take after your parents? Looks, personality, interests?

B) Do functions have parents? What is a parent graph?

C) What is a child graph? Describe the similarities and differences between a parent and child graph?

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