MATH 110 — Module 1 Exam (Respondus LockDown + Webcam) 2026 Update | 40 Questions | 100 pts
MATH 110 — MODULE 1 EXAM
REQUIRES RESPONDUS LOCKDOWN BROWSER + WEBCAM | 2026 UPDATE | 100% CORRECT
College Algebra & Precalculus • Functions · Polynomials · Rational/Radical · Exponential/Logarithmic
Aligned with 2026 | 2027 academic standards • Proctored — high academic integrity required
Questions 40 multiple-choice (4 sections) Time (suggested) 90 minutes
Points 100 (2.5 pts per question) Passing ≥ 70 (Proficient)
Cognitive Mix 30% recall · 50% application · 20% analysis Format 75% scenario / 25% direct
Proctoring Respondus LockDown + Webcam Calculator Approved scientific/graphing
Examination Instructions
This Module 1 Exam is administered under Respondus LockDown Browser with webcam monitoring to ensure
academic integrity. Questions are designed to test deep conceptual understanding and multi-step cognitive
application rather than rote recall. Rationales include step-by-step algebraic manipulations and explicitly
identify the common student errors that produce each distractor (e.g., failing to check for extraneous solutions
in radical equations, misapplying logarithm properties, incorrect domain restrictions for rational functions, or
sign errors in transformations). Section 4 integrates 2026|2027 modern computational contexts such as
calculus-ready function analysis, contemporary data modeling, and graphing-utility interpretations.
Section 1: Functions, Domain/Range, and Transformations (Q1–Q10)
Function notation, composite and inverse functions, domain and range (algebraic and graphical), and
horizontal/vertical transformations, reflections, and stretches.
Q1. Let f(x) = 2x + 3 and g(x) = x² − 1. Compute the composite function (f ■ g)(x) and evaluate at x = 2.
A. 9 [CORRECT]
B. 7
C. 11
D. 5
Correct Answer: A — 9
Rationale: (f ■ g)(x) = f(g(x)) = f(x²−1) = 2(x²−1) + 3 = 2x² + 1. At x = 2: 2(4) + 1 = 9. B computes g(f(2)); C evaluates
f(x)·g(x); D returns g(2).
Q2. Let f(x) = 3x − 5. Find the inverse function f■¹(x).
A. f■¹(x) = (x + 5)/3 [CORRECT]
B. f■¹(x) = (x − 5)/3
C. f■¹(x) = 1/(3x − 5)
D. f■¹(x) = 3x + 5
Correct Answer: A — f■¹(x) = (x + 5)/3
Rationale: Set y = 3x − 5, swap x and y: x = 3y − 5, solve for y: y = (x + 5)/3. So f■¹(x) = (x + 5)/3. B has a sign error; C
computes the reciprocal; D does not invert.
Q3. Find the domain of f(x) = √(2x − 6).
A. [3, ∞) [CORRECT]
B. (3, ∞)
Proctored Exam • College Algebra & Precalculus • 100% Correct Solutions Page 1
, MATH 110 — Module 1 Exam (Respondus LockDown + Webcam) 2026 Update | 40 Questions | 100 pts
C. (−∞, 3]
D. [0, ∞)
Correct Answer: A — [3, ∞)
Rationale: The radicand must be ≥ 0: 2x − 6 ≥ 0 → x ≥ 3. Domain = [3, ∞). B excludes x = 3 (where the function is
defined); C reverses the inequality; D ignores the inner expression.
Q4. Find the domain of f(x) = (x + 2) / (x² − 9).
A. All real numbers except x = 3 and x = −3 [CORRECT]
B. All real numbers except x = 3
C. All real numbers except x = −3
D. All real numbers
Correct Answer: A — All real numbers except x = 3 and x = −3
Rationale: Set the denominator ≠ 0: x² − 9 ≠ 0 → x ≠ ±3. Domain = all reals except ±3. B ignores the negative root; C
ignores the positive root; D allows division by zero.
Q5. The graph of y = f(x) is shifted 2 units right and 3 units down. The equation of the transformed graph is:
A. y = f(x − 2) − 3 [CORRECT]
B. y = f(x + 2) − 3
C. y = f(x − 2) + 3
D. y = f(x + 2) + 3
Correct Answer: A — y = f(x − 2) − 3
Rationale: A horizontal shift right by h is f(x − h); a vertical shift down by k is −k. So y = f(x − 2) − 3. B reverses the
horizontal direction; C reverses the vertical direction; D reverses both.
Q6. The graph of y = f(x) is reflected across the x-axis. The equation is:
A. y = −f(x) [CORRECT]
B. y = f(−x)
C. y = −f(−x)
D. y = f(x) + 1
Correct Answer: A — y = −f(x)
Rationale: Reflecting across the x-axis negates the output: y = −f(x). B reflects across the y-axis; C reflects across
both axes; D shifts vertically.
Q7. Given f(x) = x², the graph of g(x) = (x − 4)² is:
A. f shifted 4 units right [CORRECT]
B. f shifted 4 units left
C. f shifted 4 units up
D. f shifted 4 units down
Correct Answer: A — f shifted 4 units right
Rationale: g(x) = (x − 4)² has the form f(x − h) with h = 4, indicating a 4-unit right shift. B confuses the sign of h; C/D
misinterpret as a vertical shift.
Q8. The graph of y = −2√x is obtained from y = √x by:
A. Reflecting across the x-axis and stretching vertically by a factor of 2 [CORRECT]
B. Reflecting across the y-axis and stretching vertically by 2
C. Shifting down 2 units
D. Compressing horizontally by 2
Proctored Exam • College Algebra & Precalculus • 100% Correct Solutions Page 2
MATH 110 — MODULE 1 EXAM
REQUIRES RESPONDUS LOCKDOWN BROWSER + WEBCAM | 2026 UPDATE | 100% CORRECT
College Algebra & Precalculus • Functions · Polynomials · Rational/Radical · Exponential/Logarithmic
Aligned with 2026 | 2027 academic standards • Proctored — high academic integrity required
Questions 40 multiple-choice (4 sections) Time (suggested) 90 minutes
Points 100 (2.5 pts per question) Passing ≥ 70 (Proficient)
Cognitive Mix 30% recall · 50% application · 20% analysis Format 75% scenario / 25% direct
Proctoring Respondus LockDown + Webcam Calculator Approved scientific/graphing
Examination Instructions
This Module 1 Exam is administered under Respondus LockDown Browser with webcam monitoring to ensure
academic integrity. Questions are designed to test deep conceptual understanding and multi-step cognitive
application rather than rote recall. Rationales include step-by-step algebraic manipulations and explicitly
identify the common student errors that produce each distractor (e.g., failing to check for extraneous solutions
in radical equations, misapplying logarithm properties, incorrect domain restrictions for rational functions, or
sign errors in transformations). Section 4 integrates 2026|2027 modern computational contexts such as
calculus-ready function analysis, contemporary data modeling, and graphing-utility interpretations.
Section 1: Functions, Domain/Range, and Transformations (Q1–Q10)
Function notation, composite and inverse functions, domain and range (algebraic and graphical), and
horizontal/vertical transformations, reflections, and stretches.
Q1. Let f(x) = 2x + 3 and g(x) = x² − 1. Compute the composite function (f ■ g)(x) and evaluate at x = 2.
A. 9 [CORRECT]
B. 7
C. 11
D. 5
Correct Answer: A — 9
Rationale: (f ■ g)(x) = f(g(x)) = f(x²−1) = 2(x²−1) + 3 = 2x² + 1. At x = 2: 2(4) + 1 = 9. B computes g(f(2)); C evaluates
f(x)·g(x); D returns g(2).
Q2. Let f(x) = 3x − 5. Find the inverse function f■¹(x).
A. f■¹(x) = (x + 5)/3 [CORRECT]
B. f■¹(x) = (x − 5)/3
C. f■¹(x) = 1/(3x − 5)
D. f■¹(x) = 3x + 5
Correct Answer: A — f■¹(x) = (x + 5)/3
Rationale: Set y = 3x − 5, swap x and y: x = 3y − 5, solve for y: y = (x + 5)/3. So f■¹(x) = (x + 5)/3. B has a sign error; C
computes the reciprocal; D does not invert.
Q3. Find the domain of f(x) = √(2x − 6).
A. [3, ∞) [CORRECT]
B. (3, ∞)
Proctored Exam • College Algebra & Precalculus • 100% Correct Solutions Page 1
, MATH 110 — Module 1 Exam (Respondus LockDown + Webcam) 2026 Update | 40 Questions | 100 pts
C. (−∞, 3]
D. [0, ∞)
Correct Answer: A — [3, ∞)
Rationale: The radicand must be ≥ 0: 2x − 6 ≥ 0 → x ≥ 3. Domain = [3, ∞). B excludes x = 3 (where the function is
defined); C reverses the inequality; D ignores the inner expression.
Q4. Find the domain of f(x) = (x + 2) / (x² − 9).
A. All real numbers except x = 3 and x = −3 [CORRECT]
B. All real numbers except x = 3
C. All real numbers except x = −3
D. All real numbers
Correct Answer: A — All real numbers except x = 3 and x = −3
Rationale: Set the denominator ≠ 0: x² − 9 ≠ 0 → x ≠ ±3. Domain = all reals except ±3. B ignores the negative root; C
ignores the positive root; D allows division by zero.
Q5. The graph of y = f(x) is shifted 2 units right and 3 units down. The equation of the transformed graph is:
A. y = f(x − 2) − 3 [CORRECT]
B. y = f(x + 2) − 3
C. y = f(x − 2) + 3
D. y = f(x + 2) + 3
Correct Answer: A — y = f(x − 2) − 3
Rationale: A horizontal shift right by h is f(x − h); a vertical shift down by k is −k. So y = f(x − 2) − 3. B reverses the
horizontal direction; C reverses the vertical direction; D reverses both.
Q6. The graph of y = f(x) is reflected across the x-axis. The equation is:
A. y = −f(x) [CORRECT]
B. y = f(−x)
C. y = −f(−x)
D. y = f(x) + 1
Correct Answer: A — y = −f(x)
Rationale: Reflecting across the x-axis negates the output: y = −f(x). B reflects across the y-axis; C reflects across
both axes; D shifts vertically.
Q7. Given f(x) = x², the graph of g(x) = (x − 4)² is:
A. f shifted 4 units right [CORRECT]
B. f shifted 4 units left
C. f shifted 4 units up
D. f shifted 4 units down
Correct Answer: A — f shifted 4 units right
Rationale: g(x) = (x − 4)² has the form f(x − h) with h = 4, indicating a 4-unit right shift. B confuses the sign of h; C/D
misinterpret as a vertical shift.
Q8. The graph of y = −2√x is obtained from y = √x by:
A. Reflecting across the x-axis and stretching vertically by a factor of 2 [CORRECT]
B. Reflecting across the y-axis and stretching vertically by 2
C. Shifting down 2 units
D. Compressing horizontally by 2
Proctored Exam • College Algebra & Precalculus • 100% Correct Solutions Page 2
