Content review: Function Comparison Mission
Status: Published — approved by the creator. Mastery threshold 80% (provisional).
Round 1 of 3
The crossing lines
The function f(x) = −5x + 3 is compared with its parent function m(x) = x.
Input x: → Output y:
- f(x) = −5x + 3
- m(x) = x
From original
- Round title, situation, both functions, inputs
- Answer choices A–D and correct answer
- Wrong-choice and correct feedback
- Explanation prompt, placeholder and “add a sentence” message
- Open Desmos link
⚠ Reconstructed — needs approval
- Native graphs (added by creator request)
- Per-output-box feedback and common-error messages
- Misconception tags for wrong outputs and wrong choices
- “Explanation saved” confirmation
Step 1 · f(−1) =
Find f(−1). Use f(x) = −5x + 3 with x = −1.
Answer: 8
✓ Correct: Correct.
✗ Incorrect: f(−1) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If -2: Check the signs: −5 · (−1) = +5, so f(−1) = 5 + 3.
✗ If -1: −1 is the input. Substitute it into f(x) = −5x + 3 to find the output.
Step 2 · m(−1) =
Find m(−1). Use m(x) = x with x = −1.
Answer: -1
✓ Correct: Correct.
✗ Incorrect: m(−1) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If 1: m(x) = x gives back the input exactly, including its sign.
Step 3 · f(0) =
Find f(0). Use f(x) = −5x + 3 with x = 0.
Answer: 3
✓ Correct: Correct.
✗ Incorrect: f(0) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If 0: 0 is the input. Substitute it into f(x) = −5x + 3: the output is the y-intercept.
Step 4 · m(0) =
Find m(0). Use m(x) = x with x = 0.
Answer: 0
✓ Correct: Correct.
✗ Incorrect: m(0) needs another look. In Desmos, enter each function with the given input, then check your table.
Step 5 · Which statement is true?
Which statement is true?
- A. f(−1) = m(−1)
- B. f(−1) < m(−1)
- C. f(0) < m(0)
- D. f(0) > m(0) ✓
Answer: f(0) > m(0)
✓ Correct: Correct: f(0) = 3 > 0 = m(0). The lines cross, so their order depends on the input.
✗ Incorrect: At x = 0, f(0) = 3 and m(0) = 0. Look at which point is higher on the y-axis.
Step 6 · Explain using the two outputs at the same input
Explain using the two outputs at the same input.
Answer: Written explanation — saved for teacher review, not auto-scored
✓ Correct: Explanation saved. Your teacher will review it.
✗ Incorrect: Your values and choice are correct. Add a sentence that names the two outputs and explains the inequality.
Round 2 of 3
The V-shaped graphs
The pictured V has its vertex at (0, 0), so f(x) = |x|. Compare it with g(x) = |x| + 4.
Input x: → Output y:
- f(x) = |x|
- g(x) = |x| + 4
From original
- Round title, situation, both functions, inputs
- Answer choices A–D and correct answer
- Wrong-choice and correct feedback
- Explanation prompt, placeholder and “add a sentence” message
- Open Desmos link
⚠ Reconstructed — needs approval
- Native graphs (added by creator request)
- Per-output-box feedback and common-error messages
- Misconception tags for wrong outputs and wrong choices
- “Explanation saved” confirmation
Step 1 · f(3) =
Find f(3). Use f(x) = |x| with x = 3.
Answer: 3
✓ Correct: Correct.
✗ Incorrect: f(3) needs another look. In Desmos, enter each function with the given input, then check your table.
Step 2 · g(3) =
Find g(3). Use g(x) = |x| + 4 with x = 3.
Answer: 7
✓ Correct: Correct.
✗ Incorrect: g(3) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If 3: |3| = 3, then add the 4: g(3) is four units above f(3).
Step 3 · f(0) =
Find f(0). Use f(x) = |x| with x = 0.
Answer: 0
✓ Correct: Correct.
✗ Incorrect: f(0) needs another look. In Desmos, enter each function with the given input, then check your table.
Step 4 · g(0) =
Find g(0). Use g(x) = |x| + 4 with x = 0.
Answer: 4
✓ Correct: Correct.
✗ Incorrect: g(0) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If 0: |0| = 0, then add the 4. The vertex of g is at (0, 4).
Step 5 · Which statement is true?
Which statement is true?
- A. f(3) = g(3)
- B. f(3) > g(3)
- C. f(3) < g(3) ✓
- D. f(0) = g(0)
Answer: f(3) < g(3)
✓ Correct: Correct: f(3) = 3 < 7 = g(3). The +4 shifts every point of g four units above f.
✗ Incorrect: At x = 3, f(3) = 3 and g(3) = 7. Adding 4 moves the V four units up.
Step 6 · Explain using the two outputs at the same input
Explain using the two outputs at the same input.
Answer: Written explanation — saved for teacher review, not auto-scored
✓ Correct: Explanation saved. Your teacher will review it.
✗ Incorrect: Your values and choice are correct. Add a sentence that names the two outputs and explains the inequality.
Round 3 of 3
Another V-shaped comparison
The graph shows f(x) = |x| + 2 with vertex (0, 2). The other function is g(x) = |x| + 5. Graph both V-shaped functions and compare.
Input x: → Output y:
- f(x) = |x| + 2
- g(x) = |x| + 5
From original
- Round title, situation, both functions, inputs
- Answer choices A–D and correct answer
- Wrong-choice and correct feedback
- Explanation prompt, placeholder and “add a sentence” message
- Open Desmos link
⚠ Reconstructed — needs approval
- Native graphs (added by creator request)
- Per-output-box feedback and common-error messages
- Misconception tags for wrong outputs and wrong choices
- “Explanation saved” confirmation
Step 1 · f(3) =
Find f(3). Use f(x) = |x| + 2 with x = 3.
Answer: 5
✓ Correct: Correct.
✗ Incorrect: f(3) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If 3: |3| = 3, then add the 2.
Step 2 · g(3) =
Find g(3). Use g(x) = |x| + 5 with x = 3.
Answer: 8
✓ Correct: Correct.
✗ Incorrect: g(3) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If 3: |3| = 3, then add the 5.
Step 3 · f(0) =
Find f(0). Use f(x) = |x| + 2 with x = 0.
Answer: 2
✓ Correct: Correct.
✗ Incorrect: f(0) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If 0: |0| = 0, then add the 2. The vertex of f is at (0, 2).
Step 4 · g(0) =
Find g(0). Use g(x) = |x| + 5 with x = 0.
Answer: 5
✓ Correct: Correct.
✗ Incorrect: g(0) needs another look. In Desmos, enter each function with the given input, then check your table.
✗ If 0: |0| = 0, then add the 5. The vertex of g is at (0, 5).
Step 5 · Which statement is true?
Which statement is true?
- A. f(3) = g(3)
- B. f(0) < g(0) ✓
- C. f(3) > g(3)
- D. f(0) = g(0)
Answer: f(0) < g(0)
✓ Correct: Correct: f(0) = 2 < 5 = g(0). The second V is three units higher.
✗ Incorrect: At x = 0, the vertices are at heights 2 and 5. Which one is higher?
Step 6 · Explain using the two outputs at the same input
Explain using the two outputs at the same input.
Answer: Written explanation — saved for teacher review, not auto-scored
✓ Correct: Explanation saved. Your teacher will review it.
✗ Incorrect: Your values and choice are correct. Add a sentence that names the two outputs and explains the inequality.
Final independent mastery check
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