Week 3 · Quiz

Week 3 — Quiz (auto-graded) · Functions: Notation, Domain & Range

College Algebra · MATH 120 Fall 2026 · Prof. Calloway Fictional sample

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective tested: Objective 3 — function notation; evaluating functions; domain of polynomials, rational & radical functions; operations on functions; composition.
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 3.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-03-qti.xml. AI is not permitted on quizzes (course AI policy). Every numeric answer below is pre-computed and independently re-verified (Python w03_verify.py, PASS).

Blueprint

#	Type	Concept	Objective
1	Multiple choice	Identify a function from a mapping	3
2	Multiple choice	Evaluate f(x) = 2x² − 3 at f(−2)	3
3	Multiple choice	Evaluate f(x) = 3x − 1 at f(a + 2)	3
4	Multiple choice	Domain of a polynomial (all reals)	3
5	Multiple choice	Domain of a rational function	3
6	Multiple choice	Domain of a radical function	3
7	Multiple choice	(fg)(x) for f = x + 2, g = x − 3	3
8	Multiple choice	(f/g)(x) simplified with domain restriction	3
9	Multiple choice	(f ∘ g)(2) for f(x) = x², g(x) = x + 1	3
10	Matching	Function type ↔ domain rule	3

No trick questions; distractors target the Week-3 misconceptions named in the lecture outline (f(x) as multiplication, incomplete distribution in algebraic evaluation, ≥ vs. >, dropping domain restrictions after simplification, reversing composition order).

Questions, key, and feedback

Q1 (MC). Which of the following is a function?
- A. {(1, 2), (2, 3), (1, 4)} — input 1 has two outputs
- B. {(1, 3), (2, 5), (3, 7), (4, 3)} ✅
- C. A circle centered at the origin
- D. A graph that fails the vertical line test
Feedback: In (B) every input appears exactly once, so each input gives exactly one output — the definition of a function. Note: two different inputs (1 and 4) can share the same output (3); what's forbidden is one input giving two different outputs. (A) violates this: input 1 maps to both 2 and 4.

Q2 (MC). Let f(x) = 2x² − 3. Evaluate f(−2).
- A. 5 ✅
- B. −11
- C. 11
- D. −5
Feedback: Substitute (−2) for x: f(−2) = 2(−2)² − 3. Exponent first: (−2)² = 4 (the parentheses square the negative). Then 2(4) − 3 = 8 − 3 = 5. (B: misread (−2)² as −4, giving 2(−4)−3 = −11. C: computed 2(4)+3 = 11. D: computed −(2(4)−3) = −5.)

Q3 (MC). Let f(x) = 3x − 1. Evaluate f(a + 2).
- A. 3a + 5 ✅
- B. 3a + 1
- C. 3a + 7
- D. 3a − 1
Feedback: Substitute (a + 2) everywhere x appears: f(a + 2) = 3(a + 2) − 1. Distribute the 3: 3a + 6 − 1 = 3a + 5. (B: wrote 3a + 2 − 1 = 3a + 1, failing to distribute the 3 to the 2. C: added 3(2) = 6 + 1 instead of subtracting. D: substituted but didn't handle the + 2.)

Q4 (MC). What is the domain of f(x) = x² − 4x + 1?
- A. All real numbers, (−∞, ∞) ✅
- B. x ≥ 0
- C. x ≠ 0
- D. (0, ∞)
Feedback: f(x) = x² − 4x + 1 is a polynomial — no denominators, no square roots. Any real number can be plugged in. Domain: all reals, (−∞, ∞). The other options reflect domain rules for other function types (radical or rational), not polynomials.

Q5 (MC). What is the domain of f(x) = (x + 1) / (x − 3)?
- A. All real numbers
- B. x ≠ 0
- C. x ≠ 3 ✅
- D. x ≠ −1
Feedback: Set the denominator equal to zero: x − 3 = 0 → x = 3. Exclude x = 3. Domain: all x with x ≠ 3. (B: set the numerator to zero — wrong; numerator zeros are fine. D: set x + 1 = 0, which is also the numerator.)

Q6 (MC). What is the domain of f(x) = √(x − 5)?
- A. x > 5
- B. x ≥ 5 ✅
- C. x ≥ 0
- D. All real numbers
Feedback: Set the radicand ≥ 0: x − 5 ≥ 0 → x ≥ 5. The endpoint x = 5 is included because √0 = 0 is defined — no problem there. Only negative values under the radical are forbidden. (A: uses strict inequality, excluding x = 5 incorrectly. C: set x ≥ 0 instead of solving the inequality.)

Q7 (MC). Let f(x) = x + 2 and g(x) = x − 3. What is (fg)(x)?
- A. x² − x − 6 ✅
- B. 2x − 1
- C. x² + x − 6
- D. x² − 5x − 6
Feedback: (fg)(x) = f(x) · g(x) = (x + 2)(x − 3). FOIL: x² − 3x + 2x − 6 = x² − x − 6. (B: added instead of multiplied — this is (f + g)(x). C: wrong middle term sign. D: distributed only one term.)

Q8 (MC). Let f(x) = x² − 9 and g(x) = x − 3. What is (f/g)(x), fully simplified, including any domain restriction?
- A. x + 3, no restriction
- B. x + 3, x ≠ 3 ✅
- C. (x² − 9)/(x − 3), x ≠ 3
- D. x − 3, x ≠ 3
Feedback: (f/g)(x) = (x² − 9)/(x − 3) = (x − 3)(x + 3)/(x − 3) = x + 3. BUT the restriction x ≠ 3 must still be stated — g(3) = 0 makes the original expression undefined at x = 3, even though the simplified form x + 3 is defined there. (A: simplified correctly but forgot the domain restriction. D: incorrect factoring.)

Q9 (MC). Let f(x) = x² and g(x) = x + 1. What is (f ∘ g)(2)?
- A. 5
- B. 4
- C. 6
- D. 9 ✅
Feedback: (f ∘ g)(2) = f(g(2)). Step 1 — do g first: g(2) = 2 + 1 = 3. Step 2 — feed into f: f(3) = 3² = 9. (A: reversed the order — computed (g ∘ f)(2) = g(f(2)) = g(4) = 5. B: computed f(2) = 4, stopped. C: an arithmetic error.)

Q10 (Matching). Match each function type to the correct domain rule.

Function type	Correct domain rule
Polynomial (e.g., x² − 4x + 1)	All real numbers — no restrictions
Rational (e.g., (x+1)/(x−3))	Exclude values where the denominator equals zero
Function with an even root (e.g., √(x−5))	Radicand must be greater than or equal to zero
f/g where g(x) = x − 3	Domain of f ∩ domain of g, with x ≠ 3 excluded

Feedback: Polynomial = no restrictions; rational = no zero denominators; even root = radicand ≥ 0; quotient f/g = inherit the domains of f and g plus exclude wherever g = 0.

Answer key (quick reference)

Q	Answer
1	B
2	A (5)
3	A (3a + 5)
4	A (all reals)
5	C (x ≠ 3)
6	B (x ≥ 5)
7	A (x² − x − 6)
8	B (x + 3, x ≠ 3)
9	D (9)
10	Polynomial→all reals / Rational→exclude denom zeros / Even root→radicand ≥ 0 / f/g→x ≠ 3

Quality gate (self-checked, computer-verified): each single-answer item has exactly one correct option; the matching item pairs all four 1:1. Arithmetic pre-computed and independently re-verified (w03_verify.py, PASS): Q2 2(−2)²−3 = 5; Q3 3(a+2)−1 = 3a+5; Q5 x−3=0 → x=3; Q7 (x+2)(x−3)=x²−x−6; Q8 (x²−9)/(x−3)=x+3, x≠3; Q9 g(2)=3, f(3)=9. All checks PASS. QTI parse confirmation: F-quiz-week-03-qti.xml generated by qtigen.py — see parses OK, 10 items in the verifier output.

Item-bank entries (for variants + the midterm/final)

All ten items are tagged course=MATH120 · week=3 · objective=3 · topic=functions-notation-domain-range and deposited in Item Bank: Week 3 — Functions: Notation, Domain & Range. The midterm (Week 8) and per-term variant updates draw fresh items from this bank. (Tags: q1 function-def, q2 evaluate-numeric, q3 evaluate-algebraic, q4 domain-polynomial, q5 domain-rational, q6 domain-radical, q7 operations-fg, q8 operations-quotient, q9 composition, q10 domain-matching.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 3 Quiz — Functions: Notation, Domain & Range"
assignment_group = "Quizzes"
points_possible = 10
grading_type    = points
due_offset_days = 6        # 6 days after module start (Sun Sep 20)
published       = true
shuffle_answers = true
provenance      = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"

This is the human-readable quiz with its vetted answer key and rationale. The import-ready Classic-QTI version (F-quiz-week-03-qti.xml) ships inside the course's .imscc package — it lands in the Canvas gradebook on import.

~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com