WGU C957 Module 4: Interpreting Inputs and Outputs of
Linear Functions Quiz Review- Questions and Answers/ C957
Applied Algebra Module 4 Quiz 2026-2027
This exam assesses competency in interpreting inputs and outputs of linear functions within applied contexts. It
covers function notation, domain and range restrictions, slope as a rate of change, graphing linear models, and
solving linear equations arising from real-world scenarios. The focus is on translating between verbal, tabular,
graphical, and symbolic representations to make justified predictions and decisions. It contains 49
multiple-choice questions, each with four distractors and a fully worked rationale that explains why the keyed
answer is correct. Questions are organized into clearly labelled sections that mirror the major content areas of
the course. Targeted learning outcomes include: Interpret the meaning of ordered pairs, inputs, and outputs in
contextual linear models.; Determine and justify domain and range restrictions based on real-world constraints.;
Calculate and interpret slope as a rate of change in applied problems.; Solve linear equations and inequalities
derived from contextual scenarios.. Every item has been reviewed for clinical accuracy, current guidelines, and
clarity so that students can study with confidence and self-correct as they work through the bank. Use it as a
high-yield review immediately before the exam, or as a structured practice tool during the unit - the rationales
double as concise teaching notes. The recommended writing time is 2 hours, with a passing score of Competent
(equivalent to 80% or higher). Aligned with Aligned with WGU C957 Applied Algebra Course of Study
(2026-2027) and US university undergraduate quantitative reasoning standards; competency-based assessment
Section 1: General (Questions 1-49)
1 For a linear cost function C(n)=14n+320, what does the input n=0 represent?
A) The variable cost per unit produced.
B) The total cost when zero units are produced.
C) The number of units that minimizes cost.
D) The profit when no units are sold.
Answer: B
Rationale: The input n=0 yields C(0)=320, which is the fixed cost or total cost when
zero units are produced. Option A confuses the input with the slope (14), the
variable cost per unit. Option C is incorrect because linear cost functions have no
minimum at n=0. Option D confuses cost with profit and is not represented by the
function.
2 A linear model gives distance d(t)=65t miles after t hours. What is the restricted
domain for a 4-hour trip?
A) 0 t 4
B) 0 d 260
C) t 0
D) 0 t 65
Answer: A
, Rationale: The domain represents the input t (time), and a 4-hour trip restricts t to 0 "d
t 4. Option B incorrectly restricts the output (distance) instead of the input. Option
C ignores the upper bound of the trip duration. Option D uses the rate (65) as a time
bound, which is dimensionally incorrect.
3 A line passes through (2, 7) and (6, 19). What is the rate of change?
A) 2
B) 3
C) 4
D) 6
Answer: B
Rationale: Slope = (19"7)/(6"2) = 12/4 = 3, representing the rate of change. Option
A would require a change of 2 in y for every 1 in x, which is not supported. Option
C results from incorrectly dividing 12 by 3 or using wrong points. Option D is the
change in y alone, not the rate.
4 Given f(x)=5x+40, what input yields an output of 0?
A) x = 8
B) x = 5
C) x = 8
D) x = 40
Answer: C
Rationale: Set "5x+40=0, so "5x="40 and x=8. Option A results from mis-solving
the sign. Option B comes from dividing 40 by 8 or misreading the coefficient.
Option D mistakes the y-intercept for the x-intercept.
5 A linear function has slope 4 and passes through (3, 10). What is f(0)?
A) 2
B) 2
C) 10
D) 22
Answer: A
Rationale: Using point-slope: y"10=4(x"3), so y=4x"2; thus f(0)="2. Option B is the
absolute value, ignoring the sign. Option C is the y-value at x=3, not x=0. Option D
comes from adding 12 instead of subtracting.
6 A linear model for profit P(x)=12x180. What is the break-even input?
A) x = 12
Linear Functions Quiz Review- Questions and Answers/ C957
Applied Algebra Module 4 Quiz 2026-2027
This exam assesses competency in interpreting inputs and outputs of linear functions within applied contexts. It
covers function notation, domain and range restrictions, slope as a rate of change, graphing linear models, and
solving linear equations arising from real-world scenarios. The focus is on translating between verbal, tabular,
graphical, and symbolic representations to make justified predictions and decisions. It contains 49
multiple-choice questions, each with four distractors and a fully worked rationale that explains why the keyed
answer is correct. Questions are organized into clearly labelled sections that mirror the major content areas of
the course. Targeted learning outcomes include: Interpret the meaning of ordered pairs, inputs, and outputs in
contextual linear models.; Determine and justify domain and range restrictions based on real-world constraints.;
Calculate and interpret slope as a rate of change in applied problems.; Solve linear equations and inequalities
derived from contextual scenarios.. Every item has been reviewed for clinical accuracy, current guidelines, and
clarity so that students can study with confidence and self-correct as they work through the bank. Use it as a
high-yield review immediately before the exam, or as a structured practice tool during the unit - the rationales
double as concise teaching notes. The recommended writing time is 2 hours, with a passing score of Competent
(equivalent to 80% or higher). Aligned with Aligned with WGU C957 Applied Algebra Course of Study
(2026-2027) and US university undergraduate quantitative reasoning standards; competency-based assessment
Section 1: General (Questions 1-49)
1 For a linear cost function C(n)=14n+320, what does the input n=0 represent?
A) The variable cost per unit produced.
B) The total cost when zero units are produced.
C) The number of units that minimizes cost.
D) The profit when no units are sold.
Answer: B
Rationale: The input n=0 yields C(0)=320, which is the fixed cost or total cost when
zero units are produced. Option A confuses the input with the slope (14), the
variable cost per unit. Option C is incorrect because linear cost functions have no
minimum at n=0. Option D confuses cost with profit and is not represented by the
function.
2 A linear model gives distance d(t)=65t miles after t hours. What is the restricted
domain for a 4-hour trip?
A) 0 t 4
B) 0 d 260
C) t 0
D) 0 t 65
Answer: A
, Rationale: The domain represents the input t (time), and a 4-hour trip restricts t to 0 "d
t 4. Option B incorrectly restricts the output (distance) instead of the input. Option
C ignores the upper bound of the trip duration. Option D uses the rate (65) as a time
bound, which is dimensionally incorrect.
3 A line passes through (2, 7) and (6, 19). What is the rate of change?
A) 2
B) 3
C) 4
D) 6
Answer: B
Rationale: Slope = (19"7)/(6"2) = 12/4 = 3, representing the rate of change. Option
A would require a change of 2 in y for every 1 in x, which is not supported. Option
C results from incorrectly dividing 12 by 3 or using wrong points. Option D is the
change in y alone, not the rate.
4 Given f(x)=5x+40, what input yields an output of 0?
A) x = 8
B) x = 5
C) x = 8
D) x = 40
Answer: C
Rationale: Set "5x+40=0, so "5x="40 and x=8. Option A results from mis-solving
the sign. Option B comes from dividing 40 by 8 or misreading the coefficient.
Option D mistakes the y-intercept for the x-intercept.
5 A linear function has slope 4 and passes through (3, 10). What is f(0)?
A) 2
B) 2
C) 10
D) 22
Answer: A
Rationale: Using point-slope: y"10=4(x"3), so y=4x"2; thus f(0)="2. Option B is the
absolute value, ignoring the sign. Option C is the y-value at x=3, not x=0. Option D
comes from adding 12 instead of subtracting.
6 A linear model for profit P(x)=12x180. What is the break-even input?
A) x = 12
