WGU D667 PRECALCULUS OA STUDY
GUIDE 2026PRACTICE QUESTIONS,
ANSWERS, FULLY WORKED
SOLUTIONS & RATIONALES
ABOUT THIS GUIDE
This comprehensive study guide is designed to prepare you for the WGU
D667 Precalculus Objective Assessment (OA). The exam covers the
knowledge and skills necessary to apply trigonometry, complex numbers,
and systems of equations. It represents 4 competency units and
includes 6 competencies.
EXAM OVERVIEW
Aspect Details
Course Code D667
Assessment Type Objective Assessment (OA)
Question Format Multiple-choice, multiple-select, matching
Competencies 6 competency areas
Credit Units 4 competency units
, PART 1: CORE COMPETENCY AREAS
Based on standard precalculus curricula and WGU's math course
structure, the D667 OA typically covers the following domains:
1. Functions and Their Graphs – Domain, range, transformations,
compositions, inverses
2. Polynomial and Rational Functions – Zeros, asymptotes, graphing,
operations
3. Exponential and Logarithmic Functions – Properties, equations,
applications
4. Trigonometric Functions – Unit circle, graphs, identities, equations
5. Analytic Trigonometry – Identities, formulas, solving equations
6. Systems of Equations and Matrices – Linear systems, matrices,
determinants
, PART 2: PRACTICE QUESTIONS WITH WORKED SOLUTIONS
SECTION A: FUNCTIONS AND THEIR GRAPHS (QUESTIONS 1–
20)
QUESTION 1
Which of the following relations is a function?
A) {(1, 2), (1, 3), (2, 4)}
B) {(2, 3), (3, 4), (4, 5)}
C) {(3, 5), (3, 6), (4, 7)}
D) {(1, 1), (2, 2), (1, 3)}
Answer: B) {(2, 3), (3, 4), (4, 5)}
Solution:
A function requires that each input (x-value) maps to exactly one output
(y-value).
• Option A: x = 1 maps to both 2 and 3 → NOT a function
• Option B: Each x-value (2, 3, 4) maps to exactly one y-value → IS a
function
• Option C: x = 3 maps to both 5 and 6 → NOT a function
• Option D: x = 1 maps to both 1 and 3 → NOT a function
, Rationale: A relation is a function when every element in the domain
corresponds to exactly one element in the range. The vertical line test is
a graphical way to verify this—a vertical line should intersect the graph
at most once.
QUESTION 2
Find the domain of the function: f(x)=3x+2x2−4f(x)=x2−43x+2
A) All real numbers
B) All real numbers except x = 2
C) All real numbers except x = -2
D) All real numbers except x = 2 and x = -2
Answer: D) All real numbers except x = 2 and x = -2
Solution:
For a rational function, the domain excludes values that make the
denominator zero.
Set denominator = 0:
x2−4=0x2−4=0
x2=4x2=4
x=±2x=±2
Therefore, domain is all real numbers except x = 2 and x = -2.
Rationale: Division by zero is undefined in mathematics. We must
exclude any input value that causes the denominator to equal zero. The
GUIDE 2026PRACTICE QUESTIONS,
ANSWERS, FULLY WORKED
SOLUTIONS & RATIONALES
ABOUT THIS GUIDE
This comprehensive study guide is designed to prepare you for the WGU
D667 Precalculus Objective Assessment (OA). The exam covers the
knowledge and skills necessary to apply trigonometry, complex numbers,
and systems of equations. It represents 4 competency units and
includes 6 competencies.
EXAM OVERVIEW
Aspect Details
Course Code D667
Assessment Type Objective Assessment (OA)
Question Format Multiple-choice, multiple-select, matching
Competencies 6 competency areas
Credit Units 4 competency units
, PART 1: CORE COMPETENCY AREAS
Based on standard precalculus curricula and WGU's math course
structure, the D667 OA typically covers the following domains:
1. Functions and Their Graphs – Domain, range, transformations,
compositions, inverses
2. Polynomial and Rational Functions – Zeros, asymptotes, graphing,
operations
3. Exponential and Logarithmic Functions – Properties, equations,
applications
4. Trigonometric Functions – Unit circle, graphs, identities, equations
5. Analytic Trigonometry – Identities, formulas, solving equations
6. Systems of Equations and Matrices – Linear systems, matrices,
determinants
, PART 2: PRACTICE QUESTIONS WITH WORKED SOLUTIONS
SECTION A: FUNCTIONS AND THEIR GRAPHS (QUESTIONS 1–
20)
QUESTION 1
Which of the following relations is a function?
A) {(1, 2), (1, 3), (2, 4)}
B) {(2, 3), (3, 4), (4, 5)}
C) {(3, 5), (3, 6), (4, 7)}
D) {(1, 1), (2, 2), (1, 3)}
Answer: B) {(2, 3), (3, 4), (4, 5)}
Solution:
A function requires that each input (x-value) maps to exactly one output
(y-value).
• Option A: x = 1 maps to both 2 and 3 → NOT a function
• Option B: Each x-value (2, 3, 4) maps to exactly one y-value → IS a
function
• Option C: x = 3 maps to both 5 and 6 → NOT a function
• Option D: x = 1 maps to both 1 and 3 → NOT a function
, Rationale: A relation is a function when every element in the domain
corresponds to exactly one element in the range. The vertical line test is
a graphical way to verify this—a vertical line should intersect the graph
at most once.
QUESTION 2
Find the domain of the function: f(x)=3x+2x2−4f(x)=x2−43x+2
A) All real numbers
B) All real numbers except x = 2
C) All real numbers except x = -2
D) All real numbers except x = 2 and x = -2
Answer: D) All real numbers except x = 2 and x = -2
Solution:
For a rational function, the domain excludes values that make the
denominator zero.
Set denominator = 0:
x2−4=0x2−4=0
x2=4x2=4
x=±2x=±2
Therefore, domain is all real numbers except x = 2 and x = -2.
Rationale: Division by zero is undefined in mathematics. We must
exclude any input value that causes the denominator to equal zero. The
