AFDA – Unit 8: Function Families
Unit Review
Name: _________________
Block: _____ Date:_______
Directions: Using what you know about a, h, and k shifts and the general equation for
each family, write the equation of the transformed function.
1. Linear: reflection, stretch of 6 __________________________________
2. Natural Log: stretch of 4, left 7 __________________________________
3. Common Log: reflection, down 8 ________________________________
4. Absolute Value: left 2, up 4 ____________________________________
7
5. Quadratic: compressed by , right 3 _____________________________
8
1
6. Exponential (base ): right 4, up 1 ______________________________
6
Directions: Graph the following equations and provide a written comparison of how
the graph is different from the parent function.
7. 𝑦 = −2𝑥 + 7
Family:
𝑥
𝑦
Parent Function:
𝑎=
Reflection? YES or NO
ℎ=
AOS or V.A.:
𝑘=
H.A.:
Translations from parent graph?
Inc.: ____________ Dec.: ___________
Domain: __________ Range: ________
8. 𝑦 = 3|𝑥| − 6
Family:
𝑥
𝑦
Parent Function:
𝑎=
Reflection? YES or NO
ℎ=
AOS or V.A.:
𝑘=
H.A.:
Translations from parent graph?
Inc.: ____________ Dec.: ___________
Domain: __________ Range: ________
9. 𝑦 = −(𝑥 + 3)2 + 4
Family:
𝑥
𝑦
Parent Function:
𝑎=
Reflection? YES or NO
ℎ=
AOS or V.A.:
𝑘=
H.A.:
Translations from parent graph?
Inc.: ____________ Dec.: ___________
Domain: __________ Range: ________
1
10. 𝑦 = (2)𝑥+1 − 3
4
Family:
𝑥
𝑦
Parent Function:
𝑎=
Reflection? YES or NO
ℎ=
AOS or V.A.:
𝑘=
H.A.:
Translations from parent graph?
Inc.: ____________ Dec.: ___________
Domain: __________ Range: ________
11. 𝑦 = 𝑙𝑜𝑔(𝑥 − 1) + 2
Family:
𝑥
𝑦
Parent Function:
𝑎=
Reflection? YES or NO
ℎ=
AOS or V.A.:
𝑘=
H.A.:
Translations from parent graph?
Inc.: ____________ Dec.: ___________
Domain: __________ Range: ________
Directions: Use the following information to answer the questions. Be sure to round
to three decimals unless otherwise specified.
12.
The data below shows the average growth rates of 12 Weeping Higan cherry
trees planted in Washington D.C. At the time of planting, the threes were one
year old and were all 6 feet in height.
Age of the Tree
1
2
3
4
5
6
7
8
9
10
11
(in years)
Height
6 9.5 13 15 16.6 17.5 18.5 19 19.5 19.7 19.8
(in feet)
a. What is the input?
b. What is the output?
c. What is the domain of the table?
d. What is the range of the table?
e. Enter the data in your calculator, look at the scatterplot, and describe any
patterns you see (think function families + behavior).
f. What is the equation of the regression curve of best fit? Round to three
decimals.
 What is the 𝑟 2 value? What does this mean? Round to three decimals.
g. Use your regression model and table feature to estimate the average height of
the tree at 1.5 year old. Is this interpolation or extrapolation? (Round to 1
decimal)
h. Using the regression model and table feature, estimate the age of the tree if the
average height is 10 feet.
Directions: Use the following information to answer the questions. Be sure to round to
three decimals unless otherwise specified.
13.
The following table shows the average price of a movie ticket by year beginning
in 1960 (year 0).
Years since 1960
0
10
20
30
40
50
Price of Movie
$0.50 $1.55 $2.69 $4.23 6.09 $8.23
Ticket
a. Enter the data in your calculator, look at the scatterplot, and describe any
patterns you see (think function families + behavior).
b. What is the LINEAR regression equation and 𝑟 2 value?
c. What is the EXPONENTIAL regression equation and 𝑟 2 value?
d. Which regression is the better fit for the data? Why?
e. Use the better model and table feature to estimate the price of a movie ticket in
2005. Is this interpolation or extrapolation.