WGU C957 APPLIED ALGEBRA OA EXAM
| QUESTIONS AND ANSWERS |
UPDATED 2026
Chapter 1: Functions, Variables, and Notation
1. A bakery models daily revenue 𝑅as a function of the number of cakes 𝑐sold:
𝑅(24) = 720. What does this mean?
A. The bakery sold 720 cakes in 24 days.
B. Selling 24 cakes produces $720 in revenue.
C. Each cake costs $24.
D. Revenue increases by $720 per cake.
Correct Answer: B
Rationale: The input is cakes sold (24) and the output is revenue (720).
Function notation 𝑅(𝑐)maps input to output. Choice A reverses the units; C
confuses revenue with unit cost; D describes a rate, not a total.
2. A taxi fare is 𝐹(𝑚), where 𝑚is miles traveled. Which variable is independent?
A. Fare 𝐹
B. Miles 𝑚
C. Dollars per mile
D. Travel time
Correct Answer: B
Rationale: Miles are the input selected first; the fare depends on miles.
Thus 𝑚is independent and 𝐹(𝑚)is dependent.
3. For the ordered pair (7, 42)on 𝑦 = 𝑓(𝑥), which statement is correct?
A. 𝑓(42) = 7
B. 𝑓(7) = 42
,C. 𝑓(7) = 49
D. 𝑓(42) = 35
Correct Answer: B
Rationale: An ordered pair (𝑥, 𝑦)on 𝑦 = 𝑓(𝑥)means 𝑓(𝑥) = 𝑦, so 𝑓(7) =
42.
4. Evaluate 𝑓(6)for 𝑓(𝑥) = 3𝑥 − 5.
A. 13
B. 18
C. 23
D. 31
Correct Answer: A
Rationale: 𝑓(6) = 3(6) − 5 = 18 − 5 = 13.
5. Evaluate 𝑔(−2)for 𝑔(𝑥) = 𝑥 2 + 4𝑥 + 1.
A. −11
B. −3
C. 1
D. 13
Correct Answer: B
Rationale: 𝑔(−2) = (−2)2 + 4(−2) + 1 = 4 − 8 + 1 = −3.
6. A function is defined as “doubles each input.” What operation does its inverse
perform?
A. Doubles each input.
B. Subtracts 2 from each input.
C. Adds 2 to each input.
D. Halves each input.
, Correct Answer: D
Rationale: An inverse function “undoes” the original operation. If the
original multiplies by 2, the inverse divides by 2.
7. A company uses 𝐵(𝑛)to predict total benefits cost for 𝑛employees. What is the
practical use of 𝑛(𝐵)?
A. Predict the cost of benefits for new hires.
B. Determine the number of employees the company can have if the benefits
budget is fixed.
C. Calculate the average benefits cost per employee.
D. Find the total revenue generated by employees.
Correct Answer: B
Rationale: The inverse swaps input and output. 𝑛(𝐵)takes a total benefits
cost as input and outputs the number of employees — useful for workforce
planning within a fixed budget.
8. A business has 12 employees and plans to hire 3 new employees each year.
Which function models the number of employees, 𝑁, after 𝑦years, where 𝑦 =
0represents the current year?
A. 𝑁(𝑦) = 12𝑦 + 3
B. 𝑁(𝑦) = 3𝑦 + 12
C. 𝑁(𝑦) = 12𝑦 − 3
D. 𝑁(𝑦) = 3𝑦 − 12
Correct Answer: B
Rationale: The initial value is 12 (the 𝑦-intercept when 𝑦 = 0); the rate of
change is 3 employees per year (slope). So 𝑁(𝑦) = 12 + 3𝑦.
9. The temperature is 50∘ Fand decreasing by 2∘ Fevery hour ℎ. Which function
models this scenario?
, A. 𝑇(ℎ) = 50 + 2ℎ
B. 𝑇(ℎ) = 50 − 2ℎ
C. 𝑇(ℎ) = 2ℎ − 50
D. 𝑇(ℎ) = 50ℎ − 2
Correct Answer: B
Rationale: Initial temperature is 50; the temperature decreases, so
subtract 2ℎ. Thus 𝑇(ℎ) = 50 − 2ℎ.
10. The cost to mail a package is 𝐶(𝑧) = 2.50 + 0.08𝑧, where 𝑧is weight in
ounces. What is the cost to mail a 14-ounce package?
A. $2.58
B. $3.62
C. $13.24
D. $14.20
Correct Answer: B
Rationale: 𝐶(14) = 2.50 + 0.08(14) = 2.50 + 1.12 = 3.62.
11. Which of the following represents a function?
A. Input: a student’s age; Output: the number of siblings the student has.
B. Input: a person’s height; Output: their weight.
C. Input: a ZIP code; Output: the state containing that ZIP code.
D. Input: a city; Output: the number of hospitals in that city.
Correct Answer: C
Rationale: A function requires each input to map to exactly one output. A
ZIP code uniquely determines a state. The other options may have multiple
outputs for one input.
12. A function 𝑓(𝑥)is defined by the table:
| QUESTIONS AND ANSWERS |
UPDATED 2026
Chapter 1: Functions, Variables, and Notation
1. A bakery models daily revenue 𝑅as a function of the number of cakes 𝑐sold:
𝑅(24) = 720. What does this mean?
A. The bakery sold 720 cakes in 24 days.
B. Selling 24 cakes produces $720 in revenue.
C. Each cake costs $24.
D. Revenue increases by $720 per cake.
Correct Answer: B
Rationale: The input is cakes sold (24) and the output is revenue (720).
Function notation 𝑅(𝑐)maps input to output. Choice A reverses the units; C
confuses revenue with unit cost; D describes a rate, not a total.
2. A taxi fare is 𝐹(𝑚), where 𝑚is miles traveled. Which variable is independent?
A. Fare 𝐹
B. Miles 𝑚
C. Dollars per mile
D. Travel time
Correct Answer: B
Rationale: Miles are the input selected first; the fare depends on miles.
Thus 𝑚is independent and 𝐹(𝑚)is dependent.
3. For the ordered pair (7, 42)on 𝑦 = 𝑓(𝑥), which statement is correct?
A. 𝑓(42) = 7
B. 𝑓(7) = 42
,C. 𝑓(7) = 49
D. 𝑓(42) = 35
Correct Answer: B
Rationale: An ordered pair (𝑥, 𝑦)on 𝑦 = 𝑓(𝑥)means 𝑓(𝑥) = 𝑦, so 𝑓(7) =
42.
4. Evaluate 𝑓(6)for 𝑓(𝑥) = 3𝑥 − 5.
A. 13
B. 18
C. 23
D. 31
Correct Answer: A
Rationale: 𝑓(6) = 3(6) − 5 = 18 − 5 = 13.
5. Evaluate 𝑔(−2)for 𝑔(𝑥) = 𝑥 2 + 4𝑥 + 1.
A. −11
B. −3
C. 1
D. 13
Correct Answer: B
Rationale: 𝑔(−2) = (−2)2 + 4(−2) + 1 = 4 − 8 + 1 = −3.
6. A function is defined as “doubles each input.” What operation does its inverse
perform?
A. Doubles each input.
B. Subtracts 2 from each input.
C. Adds 2 to each input.
D. Halves each input.
, Correct Answer: D
Rationale: An inverse function “undoes” the original operation. If the
original multiplies by 2, the inverse divides by 2.
7. A company uses 𝐵(𝑛)to predict total benefits cost for 𝑛employees. What is the
practical use of 𝑛(𝐵)?
A. Predict the cost of benefits for new hires.
B. Determine the number of employees the company can have if the benefits
budget is fixed.
C. Calculate the average benefits cost per employee.
D. Find the total revenue generated by employees.
Correct Answer: B
Rationale: The inverse swaps input and output. 𝑛(𝐵)takes a total benefits
cost as input and outputs the number of employees — useful for workforce
planning within a fixed budget.
8. A business has 12 employees and plans to hire 3 new employees each year.
Which function models the number of employees, 𝑁, after 𝑦years, where 𝑦 =
0represents the current year?
A. 𝑁(𝑦) = 12𝑦 + 3
B. 𝑁(𝑦) = 3𝑦 + 12
C. 𝑁(𝑦) = 12𝑦 − 3
D. 𝑁(𝑦) = 3𝑦 − 12
Correct Answer: B
Rationale: The initial value is 12 (the 𝑦-intercept when 𝑦 = 0); the rate of
change is 3 employees per year (slope). So 𝑁(𝑦) = 12 + 3𝑦.
9. The temperature is 50∘ Fand decreasing by 2∘ Fevery hour ℎ. Which function
models this scenario?
, A. 𝑇(ℎ) = 50 + 2ℎ
B. 𝑇(ℎ) = 50 − 2ℎ
C. 𝑇(ℎ) = 2ℎ − 50
D. 𝑇(ℎ) = 50ℎ − 2
Correct Answer: B
Rationale: Initial temperature is 50; the temperature decreases, so
subtract 2ℎ. Thus 𝑇(ℎ) = 50 − 2ℎ.
10. The cost to mail a package is 𝐶(𝑧) = 2.50 + 0.08𝑧, where 𝑧is weight in
ounces. What is the cost to mail a 14-ounce package?
A. $2.58
B. $3.62
C. $13.24
D. $14.20
Correct Answer: B
Rationale: 𝐶(14) = 2.50 + 0.08(14) = 2.50 + 1.12 = 3.62.
11. Which of the following represents a function?
A. Input: a student’s age; Output: the number of siblings the student has.
B. Input: a person’s height; Output: their weight.
C. Input: a ZIP code; Output: the state containing that ZIP code.
D. Input: a city; Output: the number of hospitals in that city.
Correct Answer: C
Rationale: A function requires each input to map to exactly one output. A
ZIP code uniquely determines a state. The other options may have multiple
outputs for one input.
12. A function 𝑓(𝑥)is defined by the table:
