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MATH133 Unit 4: Functions and Their Graphs
Individual Project Assignment: Version 2A
IMPORTANT: Please see Question 3 under Problem 2 for special instructions for this
week’s IP assignment. This is mandatory.
Show all of your work details, explanations, and answers on the Unit 4 IP Answer Form
provided.
Problem 1: Children’s Growth
A study of the data representing the approximate average heights of children from birth to 12
years (144 months) has shown the following two equations. The function
is the radical
function representing the girls’ heights in inches after x months, and the function
function representing the boys’ heights in inches after x months (
( )
√
( )
√
is the radical
months).
1. Choose five different values of x between 0 and 144 months, and calculate the values of each of
these functions for the chosen x values. Show all of your work and display these calculated values
of
( ) and
( ) in “t-tables” in the Answer Form supplied.
2. Use these five different values of x and the corresponding calculated values of both functions,
together with Excel or another graphing utility, to draw the graphs of these two functions. These
graphs should be drawn on the same coordinate system so that the two functions can be easily
compared. Insert those graphs into the Answer Form.
3. Set the two functions equal to each other, and solve the resulting radical equation for x. This
value of x will be the age in months when boys and girls are the same height. (Show all of the
steps for solving this radical equation on the Answer Form provided.)
4. What is the height in inches when boys and girls (according to these radical functions) are the
same height? (Show all of your work on the Answer Form provided.)
5. Based on each of the two radical functions above, what is the average change in height per
month for girls and the average change in height per month for boys between the two values of
x (x = 30 months and x = 60 months)? (Show all of your work on the Answer Form provided.)
Page 1 of 3
6. Describe the transformations of the radical function ( )
√ that will result in each of these
functions.
7. Which intellipath Learning Nodes helped you with this problem?
Problem 2: Average Cost
Your company is making a product item. The fixed costs for making this product are b, and the variable
costs are mx, where x is the number of items produced. The cost function is the following linear function:
( )
The average cost is the total costs divided by the number of items produced, which is a rational function,
as follows:
̅
1. Based on the first letter of your last name, choose values for m and b from the following tables
(Neither m nor b has to be a whole number):
First letter of your last name
Possible values for m
A–F
$10–$19
G–L
$20–$29
M–R
$30–$39
S–Z
$40–$49
First letter of your last name
Possible values for b
A–F
$100–$149
G–L
$150–$199
M–R
$200–$299
S–Z
$300–$399
2. Make up the type of company and a product that you think fits the values of m and b that you
have chosen in Question 1, and briefly describe the company and product. (There is no wrong
Page 2 of 3
answer except to not answer the question. Be creative in developing your scenario, but do not
overdo it.)
3. Important: By Wednesday night at midnight, submit in a Word document only your name
and your chosen values for m and b. Submit this in the Unit 4 submissions area. This
submitted Word document will be used to determine the Last Day of Attendance for
government reporting purposes.
4. Choose five values of x < 50, and calculate the corresponding values of ̅ ( ). Display these x and
̅ ( ) values in a t-table. (Show all of your work details for these calculations. Please review this
Web site to see how to type mathematics using the keyboard symbols.)
5. Using Excel or another graphing utility, draw the graph of your average cost function, as follows:
̅
6. What happens to your average cost rational function when x gets very large? Explain your
answer.
7. How many items must be produced before the average cost is 1.5 times your chosen value of m?
(Show all of your work.)
8. Describe the transformations of the rational function ( )
that will result in your average
cost function. (Hint: What transformation types are used to get from ( )
to ( )
( )?)
9. Does your average cost function have a horizontal asymptote? If so, what is that horizontal
asymptote equation? (Explain your answer.)
10. Which intellipath Learning Nodes helped you with this problem?
Reference
Formatting math as text. (n.d.). Retrieved from the Purple Math Web site:
http://www.purplemath.com/modules/mathtext.htm
Page 3 of 3
MATH133 Unit 4: Functions and Their Graphs
Individual Project Assignment: Version 2A
Name (Required): __________________________________________________
IMPORTANT: Please see Question 3 under Problem 2 for special instructions for this
week’s IP assignment. This is mandatory.
Show all of your work details for these calculations. Please review this Web site to see how to
type mathematics using the keyboard symbols. Handwritten scanned work is not acceptable for
AIU Online.
Problem 1: Children’s Growth
𝑦 = ℎ𝑔 (𝑥) = 3.08√𝑥 + 18.97
𝑦 = ℎ𝑏 (𝑥) = 2.87√𝑥 + 20.08
1. (Show all your work, and display these calculated values of 𝑦 = ℎ𝑔 (𝑥) and 𝑦 = ℎ𝑏 (𝑥)
in the t-tables below).
𝑥
ℎ𝑔
ℎ𝑏
2. (Insert the graphs below.)
DRAFT
Page 1 of 5
3. (Show all the steps for solving this radical equation on the Answer Form provided.)
4. (Show all your work on the Answer Form provided.)
5. (Show all your work on the Answer Form provided.)
6. Describe the transformations of the of the radical function, 𝑓(𝑥) = √𝑥, that will result in
each of these functions.
DRAFT
Page 2 of 5
𝑦 = ℎ𝑔 (𝑥) = 3.08√𝑥 + 18.97
𝑦 = ℎ𝑏 (𝑥) = 2.87√𝑥 + 20.08
7. (State which intellipath Learning Nodes helped you with this problem.)
Problem 2: Average Cost
𝐶̅ =
𝑚𝑥 + 𝑏
𝑏
= 𝑚 + ,𝑥 ≥ 1
𝑥
𝑥
1. Based on the first letter of your last name, choose values for m and b from the following tables
(Neither m nor b has to be a whole number):
DRAFT
First letter of your last name
Possible values for m
A–F
$10–$19
G–L
$20–$29
M–R
$30–$39
S–Z
$40–$49
First letter of your last name
Possible values for b
A–F
$100–$149
G–L
$150–$199
M–R
$200–$299
S–Z
$300–$399
Page 3 of 5
2. (Briefly describe the company and product.)
3. (IMPORTANT) By Wednesday night at midnight submit in the Unit 4 submissions
area a Word document stating ONLY your name and your chosen values for 𝒎 and
𝒃 above. (This submitted Word document will be used to determine the Last Day of
Attendance for government reporting purposes.)
4. Choose five values of x < 50, and calculate the corresponding values of 𝐶̅ (𝑥). Display these x and
𝐶̅ (𝑥) values in a t-table. (Show all of your work details for these calculations. Please review this
Web site to see how to type mathematics using the keyboard symbols.)
𝑥
𝐶̅ (𝑥)
5. (Insert the graph below.)
DRAFT
Page 4 of 5
6. (Explain your answer.)
7. (Show all of your work.)
8. (Describe the transformations.)
9. (Explain your answer.)
10. (State the intellipath Learning Nodes that helped you with this problem.)
Reference
Formatting math as text. (n.d.). Retrieved from the Purple Math Web site:
http://www.purplemath.com/modules/mathtext.htm
DRAFT
Page 5 of 5

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