Content review: Graph Detective: Domain & Range
Status: Draft — not approved for publication. Mastery threshold 80% (provisional).
Clue 1
Traveling bus
Hours since departure and distance remaining (miles).
Input x: Hours → Output y: Miles remaining
From original
- Title, description, graph and axes
- Table inputs
- Domain/range question and choices A–D
- Correct answers (accepted by the live mission)
- “Use the leftmost, rightmost, lowest, and highest points.”
- “Correct! You uncovered a word.”
⚠ Reconstructed — needs approval
- Table answers read from plotted points (confirmed by live mission)
- Per-cell table hint wording
- Domain/range-swap feedback wording
- Misconception tags per wrong choice
Step 1 · Miles remaining at 0 hours
Miles remaining when Hours = 0
Answer: 300
✓ Correct: Correct.
✗ Incorrect: Find 0 on the Hours axis, move straight up to the plotted point, and read its Miles remaining value.
✗ If 0: 0 is the Hours value (x). The table asks for the Miles remaining value (y) at that point — read up to the plotted point.
Step 2 · Miles remaining at 3 hours
Miles remaining when Hours = 3
Answer: 150
✓ Correct: Correct.
✗ Incorrect: Find 3 on the Hours axis, move straight up to the plotted point, and read its Miles remaining value.
✗ If 3: 3 is the Hours value (x). The table asks for the Miles remaining value (y) at that point — read up to the plotted point.
Step 3 · Miles remaining at 6 hours
Miles remaining when Hours = 6
Answer: 0
✓ Correct: Correct.
✗ Incorrect: Find 6 on the Hours axis, move straight up to the plotted point, and read its Miles remaining value.
✗ If 6: 6 is the Hours value (x). The table asks for the Miles remaining value (y) at that point — read up to the plotted point.
Step 4 · Domain and range
Which domain and range describe the entire graph?
- A. Domain: 0 ≤ x ≤ 6 Range: 0 ≤ y ≤ 300 ✓
- B. Domain: 0 ≤ x ≤ 300 Range: 0 ≤ y ≤ 6
- C. Domain: 0 ≤ x ≤ 6 Range: 50 ≤ y ≤ 300
- D. Domain: 1 ≤ x ≤ 6 Range: 0 ≤ y ≤ 250
Answer: Domain: 0 ≤ x ≤ 6 Range: 0 ≤ y ≤ 300
✓ Correct: Correct! You uncovered a word.
✗ If B: Domain refers to the x-values (Hours, read left to right). Range refers to the y-values (Miles remaining, read bottom to top). Check which values belong to each.
✗ If C: Use the leftmost, rightmost, lowest, and highest points.
✗ If D: Use the leftmost, rightmost, lowest, and highest points.
Clue 2
Frog population
Number of frogs over 20 years.
Input x: Years → Output y: Number of frogs
From original
- Title, description, graph and axes
- Table inputs
- Domain/range question and choices A–D
- Correct answers (accepted by the live mission)
- “Use the leftmost, rightmost, lowest, and highest points.”
- “Correct! You uncovered a word.”
⚠ Reconstructed — needs approval
- Table answers read from plotted points (confirmed by live mission)
- Per-cell table hint wording
- Domain/range-swap feedback wording
- Misconception tags per wrong choice
Step 1 · Number of frogs at 0 years
Number of frogs when Years = 0
Answer: 100
✓ Correct: Correct.
✗ Incorrect: Find 0 on the Years axis, move straight up to the plotted point, and read its Number of frogs value.
✗ If 0: 0 is the Years value (x). The table asks for the Number of frogs value (y) at that point — read up to the plotted point.
Step 2 · Number of frogs at 10 years
Number of frogs when Years = 10
Answer: 300
✓ Correct: Correct.
✗ Incorrect: Find 10 on the Years axis, move straight up to the plotted point, and read its Number of frogs value.
✗ If 10: 10 is the Years value (x). The table asks for the Number of frogs value (y) at that point — read up to the plotted point.
Step 3 · Number of frogs at 20 years
Number of frogs when Years = 20
Answer: 500
✓ Correct: Correct.
✗ Incorrect: Find 20 on the Years axis, move straight up to the plotted point, and read its Number of frogs value.
✗ If 20: 20 is the Years value (x). The table asks for the Number of frogs value (y) at that point — read up to the plotted point.
Step 4 · Domain and range
Which domain and range describe the entire graph?
- A. Domain: 0 ≤ x ≤ 20 Range: 0 ≤ y ≤ 500
- B. Domain: 0 ≤ x ≤ 20 Range: 100 ≤ y ≤ 500 ✓
- C. Domain: 100 ≤ x ≤ 500 Range: 0 ≤ y ≤ 20
- D. Domain: 0 ≤ x ≤ 20 Range: 100 ≤ y ≤ 600
Answer: Domain: 0 ≤ x ≤ 20 Range: 100 ≤ y ≤ 500
✓ Correct: Correct! You uncovered a word.
✗ If A: Use the leftmost, rightmost, lowest, and highest points.
✗ If C: Domain refers to the x-values (Years, read left to right). Range refers to the y-values (Number of frogs, read bottom to top). Check which values belong to each.
✗ If D: Use the leftmost, rightmost, lowest, and highest points.
Clue 3
Savings account
Weeks of saving and dollars in the account.
Input x: Weeks → Output y: Dollars saved
From original
- Title, description, graph and axes
- Table inputs
- Domain/range question and choices A–D
- Correct answers (accepted by the live mission)
- “Use the leftmost, rightmost, lowest, and highest points.”
- “Correct! You uncovered a word.”
⚠ Reconstructed — needs approval
- Table answers read from plotted points (confirmed by live mission)
- Per-cell table hint wording
- Domain/range-swap feedback wording
- Misconception tags per wrong choice
Step 1 · Dollars saved at 0 weeks
Dollars saved when Weeks = 0
Answer: 20
✓ Correct: Correct.
✗ Incorrect: Find 0 on the Weeks axis, move straight up to the plotted point, and read its Dollars saved value.
✗ If 0: 0 is the Weeks value (x). The table asks for the Dollars saved value (y) at that point — read up to the plotted point.
Step 2 · Dollars saved at 3 weeks
Dollars saved when Weeks = 3
Answer: 50
✓ Correct: Correct.
✗ Incorrect: Find 3 on the Weeks axis, move straight up to the plotted point, and read its Dollars saved value.
✗ If 3: 3 is the Weeks value (x). The table asks for the Dollars saved value (y) at that point — read up to the plotted point.
Step 3 · Dollars saved at 6 weeks
Dollars saved when Weeks = 6
Answer: 80
✓ Correct: Correct.
✗ Incorrect: Find 6 on the Weeks axis, move straight up to the plotted point, and read its Dollars saved value.
✗ If 6: 6 is the Weeks value (x). The table asks for the Dollars saved value (y) at that point — read up to the plotted point.
Step 4 · Domain and range
Which domain and range describe the entire graph?
- A. Domain: 0 ≤ x ≤ 6 Range: 0 ≤ y ≤ 80
- B. Domain: 20 ≤ x ≤ 80 Range: 0 ≤ y ≤ 6
- C. Domain: 0 ≤ x ≤ 6 Range: 20 ≤ y ≤ 80 ✓
- D. Domain: 0 ≤ x ≤ 5 Range: 20 ≤ y ≤ 70
Answer: Domain: 0 ≤ x ≤ 6 Range: 20 ≤ y ≤ 80
✓ Correct: Correct! You uncovered a word.
✗ If A: Use the leftmost, rightmost, lowest, and highest points.
✗ If B: Domain refers to the x-values (Weeks, read left to right). Range refers to the y-values (Dollars saved, read bottom to top). Check which values belong to each.
✗ If D: Use the leftmost, rightmost, lowest, and highest points.
Clue 4
Water in a tank
Hours since a tank began draining and gallons remaining.
Input x: Hours → Output y: Gallons remaining
From original
- Title, description, graph and axes
- Table inputs
- Domain/range question and choices A–D
- Correct answers (accepted by the live mission)
- “Use the leftmost, rightmost, lowest, and highest points.”
- “Correct! You uncovered a word.”
⚠ Reconstructed — needs approval
- Table answers read from plotted points (confirmed by live mission)
- Per-cell table hint wording
- Domain/range-swap feedback wording
- Misconception tags per wrong choice
Step 1 · Gallons remaining at 0 hours
Gallons remaining when Hours = 0
Answer: 80
✓ Correct: Correct.
✗ Incorrect: Find 0 on the Hours axis, move straight up to the plotted point, and read its Gallons remaining value.
✗ If 0: 0 is the Hours value (x). The table asks for the Gallons remaining value (y) at that point — read up to the plotted point.
Step 2 · Gallons remaining at 4 hours
Gallons remaining when Hours = 4
Answer: 40
✓ Correct: Correct.
✗ Incorrect: Find 4 on the Hours axis, move straight up to the plotted point, and read its Gallons remaining value.
✗ If 4: 4 is the Hours value (x). The table asks for the Gallons remaining value (y) at that point — read up to the plotted point.
Step 3 · Gallons remaining at 8 hours
Gallons remaining when Hours = 8
Answer: 0
✓ Correct: Correct.
✗ Incorrect: Find 8 on the Hours axis, move straight up to the plotted point, and read its Gallons remaining value.
✗ If 8: 8 is the Hours value (x). The table asks for the Gallons remaining value (y) at that point — read up to the plotted point.
Step 4 · Domain and range
Which domain and range describe the entire graph?
- A. Domain: 0 ≤ x ≤ 8 Range: 0 ≤ y ≤ 80 ✓
- B. Domain: 0 ≤ x ≤ 80 Range: 0 ≤ y ≤ 8
- C. Domain: 2 ≤ x ≤ 8 Range: 0 ≤ y ≤ 60
- D. Domain: 0 ≤ x ≤ 8 Range: 20 ≤ y ≤ 80
Answer: Domain: 0 ≤ x ≤ 8 Range: 0 ≤ y ≤ 80
✓ Correct: Correct! You uncovered a word.
✗ If B: Domain refers to the x-values (Hours, read left to right). Range refers to the y-values (Gallons remaining, read bottom to top). Check which values belong to each.
✗ If C: Use the leftmost, rightmost, lowest, and highest points.
✗ If D: Use the leftmost, rightmost, lowest, and highest points.
Mystery punchline
What did the graph say to the table? → I SEE YOUR POINT! (one word per solved clue)
Final independent mastery check
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