Free Grade 3 Introduction to Function Notation in Context Common Errors: Visual Models — Recognition Lessons
Free Grade 3 lessons for Introduction to Function Notation in Context Common Errors: Visual Models — Recognition: 12 real questions with a full answer key and worked solutions. A function is a rule that turns an input into an output. The inverse function reverses it.
Free
Core
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introduction to function notation in context common errors: visual models — recognition
Explain introduction to function notation in context common errors: visual models — recognition accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to function notation in context common errors: visual models — recognition
Calculate introduction to function notation in context common errors: visual models — recognition accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to function notation in context common errors: visual models — recognition
Compare introduction to function notation in context common errors: visual models — recognition accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to function notation in context common errors: visual models — recognition
Justify introduction to function notation in context common errors: visual models — recognition accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Introduction to Function Notation in Context Common Errors: Visual Models — Recognition works
A function is a rule that turns an input into an output. The inverse function reverses it.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.f(x) = 2x − 8. Find f(2).[1]
- 2.f(x) = 6x + 4. Find f(5).[1]
- 3.f(x) = 4x − 2. Find f(-2).[1]
- 4.f(x) = 4x − 1. Find f(2).[1]
- 5.f(x) = 3x + 6. Find f(-3).[2]
- 6.f(x) = 6x + 3. Find f(3).[2]
- 7.f(x) = 3x + 4. Find f(4).[2]
- 8.f(x) = 5x − 7. Find f(4).[2]
- 9.f(x) = 2x − 7. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x − 3. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 3x + 8. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 2x − 5. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -4
Replace x with 2: 2 × 2 − 8. = -4
2. 34
Replace x with 5: 6 × 5 + 4. = 34
3. -10
Replace x with -2: 4 × (-2) − 2. = -10
4. 7
Replace x with 2: 4 × 2 − 1. = 7
5. -3
Replace x with -3: 3 × (-3) + 6. = -3
6. 21
Replace x with 3: 6 × 3 + 3. = 21
7. 16
Replace x with 4: 3 × 4 + 4. = 16
8. 13
Replace x with 4: 5 × 4 − 7. = 13
9. f⁻¹(x) = (x + 7) / 2
Write y = 2x − 7 and swap x and y. Rearrange for y: y = (x + 7) / 2.
10. f⁻¹(x) = (x + 3) / 2
Write y = 2x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 2.
11. f⁻¹(x) = (x − 8) / 3
Write y = 3x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 3.
12. f⁻¹(x) = (x + 5) / 2
Write y = 2x − 5 and swap x and y. Rearrange for y: y = (x + 5) / 2.
Worked examples
f(x) = 2x + 2. Find f(3).
- Replace x with 3: 2 × 3 + 2.
- = 8
- Answer: 8
f(x) = 2x − 6. Find f(-1).
- Replace x with -1: 2 × (-1) − 6.
- = -8
- Answer: -8
f(x) = 3x + 4. Find the inverse f⁻¹(x).
- Write y = 3x + 4 and swap x and y.
- Rearrange for y: y = (x − 4) / 3.
- Answer: f⁻¹(x) = (x − 4) / 3
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads f(3) as f × 3.
Correction: f(3) means 'put 3 into the rule'.
Reverses operations in the wrong order for the inverse.
Correction: Undo the last step first.
Teacher tips
- · Use function machines before notation.
Parent tips
- · Play 'guess my rule' with numbers.
Real-life applications
- · Converting temperatures, phone-plan costs.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Introduction to Function Notation in Context Common Errors: Visual Models — Recognition lesson really free?
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- What should a learner already know before this?
- Start with Introduction to Function Notation in Context Common Errors: Worked Examples. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
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- Move on to Introduction to Function Notation in Context Common Errors: Visual Models — Understanding, Introduction to Function Notation in Context Common Errors: Visual Models — Application, Introduction to Function Notation in Context Common Errors: Visual Models — Reasoning, Introduction to Function Notation in Context Common Errors: Visual Models — Mastery, which build directly on this idea.
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