WGU C957 Applied Algebra OA 2026/2027 | WGU
C957 Applied Algebra Objective Assessment Study
Guide, Practice Questions & Answers, Exam Prep,
Linear Equations, Functions, Systems of Equations,
Exponents, Polynomials, Quadratics, Logarithms &
Detailed Rationales
WGU C957 Applied Algebra OA 2026/2027 exam-prep material
designed for Western Governors University C957 Applied Algebra
students preparing for the Objective Assessment (OA). The resource
focuses on core applied-algebra concepts including linear equations
and inequalities, functions, systems of equations, exponents,
polynomials, factoring, quadratic equations, rational expressions,
radicals, logarithmic and exponential relationships, graph
interpretation, mathematical modeling and real-world applications. It
is structured for WGU C957 practice questions and answers, OA
preparation, study review, exam-style problem solving and detailed
rationales, helping students reinforce both computational skills and the
application of algebraic concepts.
,Question 1: Which of the following is the primary difference
between a relation and a function?
A. A function can have multiple outputs for a single input, while a relation
cannot.
B. A relation must be represented by a graph, while a function must be
represented by an equation.
C. A function relates each input to exactly one output, while a relation can
relate an input to multiple outputs.
D. A relation has a dependent variable, while a function only has an
independent variable.
CORRECT ANSWER: C. A function relates each input to exactly one
output, while a relation can relate an input to multiple outputs.
Rationale: By definition, a function is a special type of relation where every
element in the domain (input) is paired with exactly one element in the
range (output). A general relation does not have this restriction and may
map a single input to multiple outputs.
Question 2: A company's revenue is modeled by the function R(x) =
12x + 150, where x is the number of units sold. What does the
number 150 represent in this context?
A. The number of units sold.
B. The revenue when zero units are sold.
C. The rate at which revenue increases per unit sold.
D. The maximum possible revenue.
CORRECT ANSWER: B. The revenue when zero units are sold.
Rationale: In the linear function R(x) = mx + b, the constant b (150)
represents the y-intercept. In this business context, the y-intercept is the
revenue when the input (units sold) is zero.
Question 3: Evaluate the function f(x) = 2x² - 3x + 1 at x = -2.
A. 15
B. 3
C. -1
D. 11
CORRECT ANSWER: A. 15
,Rationale: Substitute x = -2 into the function: f(-2) = 2(-2)² - 3(-2) + 1 = 2(4)
+ 6 + 1 = 8 + 6 + 1 = 15.
Question 4: Which scenario best describes a variable that is
qualitative rather than quantitative?
A. The number of customers entering a store each hour.
B. The temperature of a patient in degrees Fahrenheit.
C. The brand of smartphone owned by an employee.
D. The price of a stock at market close.
CORRECT ANSWER: C. The brand of smartphone owned by an
employee.
Rationale: A qualitative variable describes a non-numeric characteristic or
category. The brand of a smartphone (e.g., Apple, Samsung) is categorical
data, whereas counts, temperatures, and prices are numerical
measurements.
Question 5: A catering company uses the function C(p) = 18p + 75
to determine the cost of serving p people. What is C(40)?
A. 720
B. 795
C. 815
D. 750
CORRECT ANSWER: B. 795
Rationale: Substitute p = 40 into the cost function: C(40) = 18(40) + 75 =
720 + 75 = 795.
Question 6: For a linear function y = mx + b, if m is negative, what
is the behavior of the function as x increases?
A. The function values increase.
B. The function values remain constant.
C. The function values decrease.
D. The function values become undefined.
CORRECT ANSWER: C. The function values decrease.
Rationale: The slope m represents the rate of change. A negative slope
indicates that as the independent variable x increases, the dependent
variable y decreases.
, Question 7: A cell phone plan charges a flat monthly fee of $35 plus
$0.10 per minute for international calls. Which function models the
total monthly cost, C(m), for m minutes of international calls?
A. C(m) = 35m + 0.10
B. C(m) = 0.10m + 35
C. C(m) = 45m
D. C(m) = 35 - 0.10m
CORRECT ANSWER: B. C(m) = 0.10m + 35
Rationale: The total cost is the sum of the fixed monthly fee ($35) and the
variable cost ($0.10 times the number of minutes). The variable cost
depends on m, so the slope is 0.10 and the y-intercept is 35.
Question 8: Which of the following equations represents a linear
function?
A. y = x³ + 2x
B. y = 5/x
C. y = 4 - 3x
D. y = 2^x
CORRECT ANSWER: C. y = 4 - 3x
Rationale: A linear function can be written in the form y = mx + b, where
the highest power of the independent variable is 1. The equation y = 4 - 3x
fits this form. The others involve cubic, rational, or exponential terms.
Question 9: The profit function for a product is P(n) = 5n - 200,
where n is the number of units sold. What is the break-even point?
A. 20 units
B. 40 units
C. 50 units
D. 200 units
CORRECT ANSWER: B. 40 units
Rationale: The break-even point occurs when profit equals zero. Set P(n) =
0: 5n - 200 = 0, so 5n = 200, and n = 40.
Question 10: Which characteristic is true of the graph of a function
that is concave down?
C957 Applied Algebra Objective Assessment Study
Guide, Practice Questions & Answers, Exam Prep,
Linear Equations, Functions, Systems of Equations,
Exponents, Polynomials, Quadratics, Logarithms &
Detailed Rationales
WGU C957 Applied Algebra OA 2026/2027 exam-prep material
designed for Western Governors University C957 Applied Algebra
students preparing for the Objective Assessment (OA). The resource
focuses on core applied-algebra concepts including linear equations
and inequalities, functions, systems of equations, exponents,
polynomials, factoring, quadratic equations, rational expressions,
radicals, logarithmic and exponential relationships, graph
interpretation, mathematical modeling and real-world applications. It
is structured for WGU C957 practice questions and answers, OA
preparation, study review, exam-style problem solving and detailed
rationales, helping students reinforce both computational skills and the
application of algebraic concepts.
,Question 1: Which of the following is the primary difference
between a relation and a function?
A. A function can have multiple outputs for a single input, while a relation
cannot.
B. A relation must be represented by a graph, while a function must be
represented by an equation.
C. A function relates each input to exactly one output, while a relation can
relate an input to multiple outputs.
D. A relation has a dependent variable, while a function only has an
independent variable.
CORRECT ANSWER: C. A function relates each input to exactly one
output, while a relation can relate an input to multiple outputs.
Rationale: By definition, a function is a special type of relation where every
element in the domain (input) is paired with exactly one element in the
range (output). A general relation does not have this restriction and may
map a single input to multiple outputs.
Question 2: A company's revenue is modeled by the function R(x) =
12x + 150, where x is the number of units sold. What does the
number 150 represent in this context?
A. The number of units sold.
B. The revenue when zero units are sold.
C. The rate at which revenue increases per unit sold.
D. The maximum possible revenue.
CORRECT ANSWER: B. The revenue when zero units are sold.
Rationale: In the linear function R(x) = mx + b, the constant b (150)
represents the y-intercept. In this business context, the y-intercept is the
revenue when the input (units sold) is zero.
Question 3: Evaluate the function f(x) = 2x² - 3x + 1 at x = -2.
A. 15
B. 3
C. -1
D. 11
CORRECT ANSWER: A. 15
,Rationale: Substitute x = -2 into the function: f(-2) = 2(-2)² - 3(-2) + 1 = 2(4)
+ 6 + 1 = 8 + 6 + 1 = 15.
Question 4: Which scenario best describes a variable that is
qualitative rather than quantitative?
A. The number of customers entering a store each hour.
B. The temperature of a patient in degrees Fahrenheit.
C. The brand of smartphone owned by an employee.
D. The price of a stock at market close.
CORRECT ANSWER: C. The brand of smartphone owned by an
employee.
Rationale: A qualitative variable describes a non-numeric characteristic or
category. The brand of a smartphone (e.g., Apple, Samsung) is categorical
data, whereas counts, temperatures, and prices are numerical
measurements.
Question 5: A catering company uses the function C(p) = 18p + 75
to determine the cost of serving p people. What is C(40)?
A. 720
B. 795
C. 815
D. 750
CORRECT ANSWER: B. 795
Rationale: Substitute p = 40 into the cost function: C(40) = 18(40) + 75 =
720 + 75 = 795.
Question 6: For a linear function y = mx + b, if m is negative, what
is the behavior of the function as x increases?
A. The function values increase.
B. The function values remain constant.
C. The function values decrease.
D. The function values become undefined.
CORRECT ANSWER: C. The function values decrease.
Rationale: The slope m represents the rate of change. A negative slope
indicates that as the independent variable x increases, the dependent
variable y decreases.
, Question 7: A cell phone plan charges a flat monthly fee of $35 plus
$0.10 per minute for international calls. Which function models the
total monthly cost, C(m), for m minutes of international calls?
A. C(m) = 35m + 0.10
B. C(m) = 0.10m + 35
C. C(m) = 45m
D. C(m) = 35 - 0.10m
CORRECT ANSWER: B. C(m) = 0.10m + 35
Rationale: The total cost is the sum of the fixed monthly fee ($35) and the
variable cost ($0.10 times the number of minutes). The variable cost
depends on m, so the slope is 0.10 and the y-intercept is 35.
Question 8: Which of the following equations represents a linear
function?
A. y = x³ + 2x
B. y = 5/x
C. y = 4 - 3x
D. y = 2^x
CORRECT ANSWER: C. y = 4 - 3x
Rationale: A linear function can be written in the form y = mx + b, where
the highest power of the independent variable is 1. The equation y = 4 - 3x
fits this form. The others involve cubic, rational, or exponential terms.
Question 9: The profit function for a product is P(n) = 5n - 200,
where n is the number of units sold. What is the break-even point?
A. 20 units
B. 40 units
C. 50 units
D. 200 units
CORRECT ANSWER: B. 40 units
Rationale: The break-even point occurs when profit equals zero. Set P(n) =
0: 5n - 200 = 0, so 5n = 200, and n = 40.
Question 10: Which characteristic is true of the graph of a function
that is concave down?
