May 30, 2012
1. Use the table to answer the questions below.
t
-6
-4
-2
0
2
4
R(t)
2
4
8
16
32
64
V(t)
4
3.2
2.4
1.6
0.8
0
Z(t)
-2
-2
-2
-2
-2
-2
a. Identify which of the function(s) above is linear. Explain your reasoning.
b. Write the equation for each linear function you found in part a.
2. Circle the letter of the correct statement.
The notation G(m) defines …
i.
the domain of the function.
ii. the range of the function.
iii. that G is the independent variable and m is the dependent variable.
iv. that G is the dependent variable and m is the independent variable.
3. Fill in numbers in the tables below so that the table on the left is a function and the table on the
right is not a function.
Input
Function
Output
-3
0
5
13
10
Not a Function
Input
Output
-3
0
5
13
10
May 30, 2012
4. Leslie has decided she would like to donate her hair to “Locks of Love”, an organization that
provides wigs to cancer patients who have lost their own hair. After 6 months of growing her hair
out, she has 5 inches of hair that she will donate. After 8 months, she has 6 inches of hair that
she will donate.
a. Identify the independent and dependent variables.
b. Write a linear equation that models the situation using function notation. Show your work.
c. What is the slope? Interpret this value in the context of the problem.
d. What is the vertical intercept? Interpret this value in the context of the problem.
e. How long will it take Leslie to have 12 inches of hair that she will donate? Show all work.
5. Sherri has been recording the amount of snow in her yard as she anxiously waits for spring. The
equation to model the amount of snow in her yard is A  d   3.065d  64.444 . A, the amount
of snow in inches, is a function of d, the time in days since Sherri started keeping track of the
snow depth.
a. Determine the horizontal intercept. Show your work and round to 2 decimals.
b. Interpret part b in the context of the problem.
May 30, 2012
c. Write a reasonable domain for the function. Use proper mathematical notation.
d. Write a reasonable range for the function. Use proper mathematical notation.
e. Evaluate A 15  . Show your work.
f. Interpret part e in the context of the problem.
g. Solve A  d   15 . Show your work.
h. Interpret part g in the context of the problem.
6. Given the parent function, f  x  , describe each transformation.
a. f  x  3   1
b. f  x   1
c.
f  x  7
May 30, 2012
7. The parent function, f  x  , is given on the graph below. Draw f  x  1  2 .
8. Johnson Incorporated makes wonderful widgets. Each widget costs $2.50 to make plus there is
a one-time setup fee of $450. Each widget will yield $7.00 in revenue. Let w, independent
variable, represent number of widgets. The dependent variables are C, cost in dollars, and R,
revenue in dollars.
a. Write the system of equations for cost and revenue to represent the information given.
b. Solve the system. Show your algebraic work.
c. Interpret the solution from part b in the context of the problem.
May 30, 2012
9. While driving to her backpack trip this summer, Ambika hit construction just past Wolf Creek
Pass. The graph below tells the story of some of her travel.
Ambika's Trip
Speed (mph) (s)
80
70
60
50
40
30
20
10
time in min (m)
5
a.
10
15
20
25
30
Fill in the blanks for the piecewise function below.
 _________
3m  100

S m  
5.5m  137.5
 _________
___  m  10
10  m  ___
___  m  25
25  m  ___
b. What is the vertical intercept? What does it mean in the context of the problem?
c. What is the slope in the last piece of the function? What does this mean in the context of the
problem?
d. Evaluate s(12) algebraically and describe what this means in the context of the problem.
May 30, 2012
10. Sandy has started an animal grooming business. From experience, she knows a cat takes 12
minutes to wash and 30 minutes to groom. She also knows that it takes 20 minutes to wash a
dog and 30 minutes to groom it. Her staff will spend at most 9 hours washing animals each
day, but at least 8 hours grooming the animals. In addition to this, the staff can handle no more
than 33 animals in a single day. How many dogs and cats can they wash and groom each day?
a. Let c represent the number of cats and d represent the number of dogs. Circle all of the
inequalities below that are needed to solve this problem.
12c  30d  540
c0
30c  30d  480
20c  12d  540
c0
c  d  33
30c  20d  480
30c  30d  480
d 0
d 0
c  d  33
12c  20d  540
b. Shade the feasible region based on the inequalities you chose in part a.
Sandy's Great Grooming
(0,33)
total
# of dogs (d)
(0,27)
(15,18)
(0,16)
washing
grooming
(16,0)
(33,0)
(45,0)
# of cats (c)
c. Sandy makes $35 on each cat she grooms and $20 on each dog. Write the objective
function for profit.
d. How many of each animal should Sandy wash and groom each day in order to maximize her
profit? Justify your answer with mathematical work.
May 30, 2012
11. Hansel and Gretel went shopping for candy. Hansel bought 2 lollipops and 6 giant chocolate
bars, spending $15.70. Gretel spent $14.60 on 4 lollipops and 5 giant chocolate bars.
a. Define the variables of the situation.
b. Write the system of equations that models the situation.
c. Solve the system of equations that you wrote in part b algebraically. Show your work.
d. Interpret part c in the context of the problem.
12. The number of asthma sufferers in the world was 84 million in 1990 and 130 million in 2001.
a. Define the variables.
b. Write an exponential function that models this situation. Show all work and round to three
decimals.
c. Using the equation written in part b, determine when the number of asthma sufferers will
reach 200 million. Show all work.
d. Write a linear function that models this situation. Show all work and round to three
decimals.
May 30, 2012
13. The earth’s atmospheric pressure is a function of the height above sea level. The pressure at
sea level (height = 0) is 1013 millibars and the pressure decreases by 14% for every kilometer
above sea level.
a. Write the exponential function with p as the pressure and h as the height above sea level
using function notation. Clearly define the variables.
b. What is the atmospheric pressure at 50 km? Round to three decimals.
c. What is the altitude at which the pressure equals 200 millibars? Show your work.
14. Use the parent function, f  x   1.5x , to answer the questions below.
a. What is the asymptote of f  x  ?
b. Write the end behavior for f  x  .
c. Write the transformed equation g  x  , if f  x  is shifted right 2 units and up 3 units.
d. What is the asymptote of g  x  ?
May 30, 2012
15. Suppose an investment pays 4.9%, and the initial investment amount is $1500. Let t be the time
in years. Round answers to 2 decimals.
A  P(1  r )t
A  Pe rt
r

A  P 1  
 n
nt
y  mx  b
a. Write the function for the value after t years if interest is compounded monthly.
b. Determine the value of the investment in part a after 5 years. Show your work.
c. Write the function for the value after t years if interest is compounded continuously.
d. After how many years will the investment in part c double in value? Show your algebraic
work.
16. Let the independent variable represent the time in years since 1974, t, and let the dependent
variable represent the total population, S for number of Sleestaks, and P for number of Pakuni.
Below are the functions for each population.
S  t   75 1.042 
t
P  t   215  22.5t
a. Interpret the rate from the function representing the Sleestak population.
b. Interpret the rate from the function representing the Pakuni population.
May 30, 2012
17. The volume, V, of a pyramid is jointly proportional to the height, h, and the square of the base
length, b.
a. Write the general equation to describe the volume of a pyramid, V, as a function of the
height, h, and the square of the base length, b.
b. If a pyramid having a height of 5 cm and a base length of 3 cm has a volume of 15 cm3, find
the constant of proportionality and write the specific equation using this value. Show your
work.
c. What is the volume of a pyramid with a height of 50cm and a base length of 36cm? Show
your work.
18. A herd of 204 wild African gazelles is introduced to a wild animal park in 1960. The population of
the gazelles, P(t), after t years since 1960 is given by P  t   0.7t 3  18.7t 2  69.5t  204 .
a. What is the maximum population reached by the Gazelles?
b. When does it reach this maximum population?
c. When will the herd reach 600 gazelles?
d. What is the range of this function?
May 30, 2012
e. Without intervention, will the herd ever be completely eliminated? Explain your reasoning.
19. Assume no transformations have been performed on functions A-I below.
A.
B.
C.
y
y
y
x
x
x
D.
E.
F.
y
y
y
x
x
x
G.
H.
y
1
x3
i.
I.
y e
x
y  ln  x 
List all of the function(s) (A-I) that are even power functions.
ii. List all of the function(s) (A-I) that are directly proportional power functions.
iii. List all of the function(s) (A-I) that are exponential.
iv. List all of the function(s) (A-I) that have the following end behavior: As x→−∞, y→0.
May 30, 2012
20. Leslie has been recording the amount of snow in her yard as she anxiously waits for spring. She
recorded the information in the table below.
Day
Amount
(inches)
0
2
5
7
10
11
13
61
57
54
48
33
27
24
a. If A, the amount of snow in inches, is a function of d, the time in days since Leslie started
keeping track of the snow depth, circle the linear regression function that represents the
data above.
A  d   6.857d  64.000
A  d   3.065d  61.000
A  d   3.065d  64.444
A  d   0.308d  20.233
b. Using the model you selected in part a, find the horizontal intercept. Round to 2 decimals.
c. Interpret part b in the context of the problem.
d. Interpret the slope of the model selected in part a in the context of the problem.
e. Solve A  d   40 . Show your work.
f. Interpret part e in the context of the problem.
g. Write the range of the model. Use proper mathematical notation.
May 30, 2012
21. Algebraically determine whether the following functions are inverses of each other. Be sure to
indicate yes, they are inverses or no, they are not inverses.
a. f  x  
1
x  3 and g  x   2x  6
2
b. f  x  
x  2 and g  x   x 2  2
c. f  x   10x  5 and g  x  
x
5
10
22. Tuition at a near-by college is represented by the function T= f(c) = 400 + 30c, where c
represents the number of credits a student takes and T represents the tuition paid in dollars.
a. From the choices below, circle the option that interprets c  f 1 T  correctly.
The cost per credit is a function of
the number of credits
The number of credits is a
function of the tuition paid
The tuition paid is a function
of the number of credits
Number of years to graduate
is a function of tuition paid
b. Find f 1 T  .
c. Evaluate f
work.
1
850 .
Explain what this means in the context of the problem. Show your
May 30, 2012
23. Suppose A  f  m  is the amount of gas (in gallons) after m (in miles) for Leslie’s car and that
f  20  15 and f 120  13 .
a. Find a linear model (without regression) for A  f  m  Show your work.
b. What is the horizontal intercept? Interpret the horizontal intercept in context.
c. What is the slope of the linear model? Interpret the slope in the context of the problem.
d. Find the inverse function of the equation from part a.
e. Evaluate f 1  0.5  .
f.
Explain what the value from part e means in the context of Leslie’s car.
May 30, 2012
24. Leslie is standing on top of a building. She plans to launch a water balloon off the building to
demonstrate that gravity works. The balloon’s height H, in feet, is represented by
H  t   16t 2  24t  54.2 , where t is time in seconds.
Round to 2 decimals.
a. Evaluate H  0  and interpret this in the context of the problem.
b. Solve H  t   0 and interpret this in the context of the problem.
c. What is the balloon’s maximum height? At what time does this occur?
d. Give a reasonable domain for this situation.