WGU C957 APPLIED ALGEBRA OA/
OBJECTIVE ASSESSMENT EXAM: (LATEST
2026/2027 UPDATE) QUESTIONS AND
VERIFIED ANSWERS| GRADE A
WGU C957 APPLIED ALGEBRA OA/
OBJECTIVE ASSESSMENT
WGU C957 Applied Algebra OA Exam 2026/2027
1. A function doubles each input. What does the inverse function do?
A. Adds 2 to each input
B. Subtracts 2 from each input
C. Squares each input
D. Halves each input
Answer: D. Halves each input
Rationale:
A function that doubles an input can be written as f(x)=2xf(x)=2x. The inverse
function, f−1(x)f−1(x), reverses the effect of the original function. Since multiplying by
2 is the original operation, the inverse divides by 2, effectively halving the input. This
ensures that f−1(f(x))=xf−1(f(x))=x, satisfying the property of inverse functions.
Halving correctly returns the original input.
,2. Sales tax in your state is 7%. Which function models the amount of sales
tax, TT, when you spend xx dollars?
A. T(x)=x+0.07T(x)=x+0.07
B. T(x)=0.7xT(x)=0.7x
C. T(x)=7xT(x)=7x
D. T(x)=0.07xT(x)=0.07x
Answer: D. T(x)=0.07xT(x)=0.07x
Rationale:
Sales tax is calculated as a percentage of the purchase amount. First, convert the
percentage to a decimal: 7% becomes 0.07. Then multiply this decimal by the amount
spent xx to find the tax. This function correctly models the proportional relationship
between the amount spent and the tax owed. It ensures that as spending increases,
the sales tax increases proportionally.
3. Your daughter babysits and charges $8 per hour. Select the function that
models the amount of money she earns when babysitting for hh hours.
A. B(h)=8+hB(h)=8+h
B. B(h)=8/hB(h)=8/h
C. B(h)=8hB(h)=8h
D. B(h)=h/8B(h)=h/8
Answer: C. B(h)=8hB(h)=8h
Rationale:
Earnings are calculated by multiplying the hourly rate by the number of hours worked.
Here, the hourly rate is $8, so for hh hours, the total earnings are 8h8h. This linear
function represents a constant rate of change, meaning for every additional hour
worked, the earnings increase by $8. The function accurately models the real-life
scenario of hourly earnings.
,4. Your business currently has 12 employees and adds 3 new employees
each year. Which function models the total number of
employees N(y)N(y) after yy years?
A. N(y)=3y−12N(y)=3y−12
B. N(y)=12y+3N(y)=12y+3
C. N(y)=12+3yN(y)=12+3y
D. N(y)=12⋅3yN(y)=12⋅3y
Answer: C. N(y)=12+3yN(y)=12+3y
Rationale:
The total number of employees is modeled by a linear function because there is a
constant addition of 3 employees per year. The initial value (intercept) is 12
employees, representing the starting number. The slope is 3, which is the rate of
change per year. By combining the initial value and the yearly increase, the
function N(y)=12+3yN(y)=12+3y accurately predicts employee count for any number
of years.
5. The temperature outside is currently 50 degrees Fahrenheit and is
decreasing by 2 degrees per hour. Which function models the
temperature T(h)T(h) after hh hours?
A. T(h)=50+2hT(h)=50+2h
B. T(h)=50−h/2T(h)=50−h/2
C. T(h)=50−2hT(h)=50−2h
D. T(h)=2h−50T(h)=2h−50
Answer: C. T(h)=50−2hT(h)=50−2h
Rationale:
This is a linear function where the initial temperature is 50°F. The temperature
decreases at a rate of 2 degrees per hour, which is represented as a negative slope.
By multiplying the rate of change by the number of hours hh and subtracting from the
initial temperature, the function gives the correct temperature at any hour. It captures
the continuous decline over time in a predictable manner.
, 6. The cost to mail a package that weighs zz ounces is given
by C(z)=2.50+0.08zC(z)=2.50+0.08z. What is the cost to mail a 14-ounce
package?
A. $2.50
B. $2.62
C. $3.50
D. $3.62
Answer: D. $3.62
Rationale:
The cost function combines a fixed base cost ($2.50) with a variable cost proportional
to the weight (0.08 per ounce).
Substituting z=14z=14 gives C(14)=2.50+0.08(14)C(14)=2.50+0.08(14). Multiplying
0.08 by 14 gives 1.12, and adding the base cost 2.50 results in 3.62. This correctly
models the total shipping cost for any package weight.
7. A car rental company charges a $25 flat fee plus $0.15 per mile driven.
Which function models the total cost, C, for driving m miles?
A) C(m)=0.15mC(m)=0.15m
B) C(m)=25m+0.15C(m)=25m+0.15
C) C(m)=25+0.15mC(m)=25+0.15m
D) C(m)=25−0.15mC(m)=25−0.15m
Answer: (C) C(m)=25+0.15mC(m)=25+0.15m
Rationale: The total cost includes a flat fee of $25, which is the initial value. Each
mile adds $0.15 to the total, representing the rate of change. A linear function
combining these two components is written as C(m)=initial value+
(rate per mile×m)=25+0.15mC(m)=initial value+(rate per mile×m)=25+0.15m. Options
A and B misplace the flat fee or rate, and D incorrectly subtracts per-mile cost.
OBJECTIVE ASSESSMENT EXAM: (LATEST
2026/2027 UPDATE) QUESTIONS AND
VERIFIED ANSWERS| GRADE A
WGU C957 APPLIED ALGEBRA OA/
OBJECTIVE ASSESSMENT
WGU C957 Applied Algebra OA Exam 2026/2027
1. A function doubles each input. What does the inverse function do?
A. Adds 2 to each input
B. Subtracts 2 from each input
C. Squares each input
D. Halves each input
Answer: D. Halves each input
Rationale:
A function that doubles an input can be written as f(x)=2xf(x)=2x. The inverse
function, f−1(x)f−1(x), reverses the effect of the original function. Since multiplying by
2 is the original operation, the inverse divides by 2, effectively halving the input. This
ensures that f−1(f(x))=xf−1(f(x))=x, satisfying the property of inverse functions.
Halving correctly returns the original input.
,2. Sales tax in your state is 7%. Which function models the amount of sales
tax, TT, when you spend xx dollars?
A. T(x)=x+0.07T(x)=x+0.07
B. T(x)=0.7xT(x)=0.7x
C. T(x)=7xT(x)=7x
D. T(x)=0.07xT(x)=0.07x
Answer: D. T(x)=0.07xT(x)=0.07x
Rationale:
Sales tax is calculated as a percentage of the purchase amount. First, convert the
percentage to a decimal: 7% becomes 0.07. Then multiply this decimal by the amount
spent xx to find the tax. This function correctly models the proportional relationship
between the amount spent and the tax owed. It ensures that as spending increases,
the sales tax increases proportionally.
3. Your daughter babysits and charges $8 per hour. Select the function that
models the amount of money she earns when babysitting for hh hours.
A. B(h)=8+hB(h)=8+h
B. B(h)=8/hB(h)=8/h
C. B(h)=8hB(h)=8h
D. B(h)=h/8B(h)=h/8
Answer: C. B(h)=8hB(h)=8h
Rationale:
Earnings are calculated by multiplying the hourly rate by the number of hours worked.
Here, the hourly rate is $8, so for hh hours, the total earnings are 8h8h. This linear
function represents a constant rate of change, meaning for every additional hour
worked, the earnings increase by $8. The function accurately models the real-life
scenario of hourly earnings.
,4. Your business currently has 12 employees and adds 3 new employees
each year. Which function models the total number of
employees N(y)N(y) after yy years?
A. N(y)=3y−12N(y)=3y−12
B. N(y)=12y+3N(y)=12y+3
C. N(y)=12+3yN(y)=12+3y
D. N(y)=12⋅3yN(y)=12⋅3y
Answer: C. N(y)=12+3yN(y)=12+3y
Rationale:
The total number of employees is modeled by a linear function because there is a
constant addition of 3 employees per year. The initial value (intercept) is 12
employees, representing the starting number. The slope is 3, which is the rate of
change per year. By combining the initial value and the yearly increase, the
function N(y)=12+3yN(y)=12+3y accurately predicts employee count for any number
of years.
5. The temperature outside is currently 50 degrees Fahrenheit and is
decreasing by 2 degrees per hour. Which function models the
temperature T(h)T(h) after hh hours?
A. T(h)=50+2hT(h)=50+2h
B. T(h)=50−h/2T(h)=50−h/2
C. T(h)=50−2hT(h)=50−2h
D. T(h)=2h−50T(h)=2h−50
Answer: C. T(h)=50−2hT(h)=50−2h
Rationale:
This is a linear function where the initial temperature is 50°F. The temperature
decreases at a rate of 2 degrees per hour, which is represented as a negative slope.
By multiplying the rate of change by the number of hours hh and subtracting from the
initial temperature, the function gives the correct temperature at any hour. It captures
the continuous decline over time in a predictable manner.
, 6. The cost to mail a package that weighs zz ounces is given
by C(z)=2.50+0.08zC(z)=2.50+0.08z. What is the cost to mail a 14-ounce
package?
A. $2.50
B. $2.62
C. $3.50
D. $3.62
Answer: D. $3.62
Rationale:
The cost function combines a fixed base cost ($2.50) with a variable cost proportional
to the weight (0.08 per ounce).
Substituting z=14z=14 gives C(14)=2.50+0.08(14)C(14)=2.50+0.08(14). Multiplying
0.08 by 14 gives 1.12, and adding the base cost 2.50 results in 3.62. This correctly
models the total shipping cost for any package weight.
7. A car rental company charges a $25 flat fee plus $0.15 per mile driven.
Which function models the total cost, C, for driving m miles?
A) C(m)=0.15mC(m)=0.15m
B) C(m)=25m+0.15C(m)=25m+0.15
C) C(m)=25+0.15mC(m)=25+0.15m
D) C(m)=25−0.15mC(m)=25−0.15m
Answer: (C) C(m)=25+0.15mC(m)=25+0.15m
Rationale: The total cost includes a flat fee of $25, which is the initial value. Each
mile adds $0.15 to the total, representing the rate of change. A linear function
combining these two components is written as C(m)=initial value+
(rate per mile×m)=25+0.15mC(m)=initial value+(rate per mile×m)=25+0.15m. Options
A and B misplace the flat fee or rate, and D incorrectly subtracts per-mile cost.
