Free Grade 3 Introduction to Function Notation in Context Essentials: Common Mistakes — Mastery Worksheets
Free Grade 3 worksheets for Introduction to Function Notation in Context Essentials: Common Mistakes — Mastery: 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.
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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 essentials: common mistakes — mastery
Explain introduction to function notation in context essentials: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to function notation in context essentials: common mistakes — mastery
Calculate introduction to function notation in context essentials: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to function notation in context essentials: common mistakes — mastery
Compare introduction to function notation in context essentials: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to function notation in context essentials: common mistakes — mastery
Justify introduction to function notation in context essentials: common mistakes — mastery 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 Essentials: Common Mistakes — Mastery 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) = 3x + 2. Find f(3).[1]
- 2.f(x) = 3x + 0. Find f(0).[1]
- 3.f(x) = 4x − 5. Find f(1).[1]
- 4.f(x) = 5x − 3. Find f(-4).[1]
- 5.f(x) = 4x + 5. Find f(3).[2]
- 6.f(x) = 2x + 5. Find f(2).[2]
- 7.f(x) = 2x − 6. Find f(4).[2]
- 8.f(x) = 6x − 1. Find f(-3).[2]
- 9.f(x) = 2x − 3. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 5x + 3. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 4x + 5. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 6x − 5. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 11
Replace x with 3: 3 × 3 + 2. = 11
2. 0
Replace x with 0: 3 × 0 + 0. = 0
3. -1
Replace x with 1: 4 × 1 − 5. = -1
4. -23
Replace x with -4: 5 × (-4) − 3. = -23
5. 17
Replace x with 3: 4 × 3 + 5. = 17
6. 9
Replace x with 2: 2 × 2 + 5. = 9
7. 2
Replace x with 4: 2 × 4 − 6. = 2
8. -19
Replace x with -3: 6 × (-3) − 1. = -19
9. f⁻¹(x) = (x + 3) / 2
Write y = 2x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 2.
10. f⁻¹(x) = (x − 3) / 5
Write y = 5x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 5.
11. f⁻¹(x) = (x − 5) / 4
Write y = 4x + 5 and swap x and y. Rearrange for y: y = (x − 5) / 4.
12. f⁻¹(x) = (x + 5) / 6
Write y = 6x − 5 and swap x and y. Rearrange for y: y = (x + 5) / 6.
Worked examples
f(x) = 4x + 2. Find f(-3).
- Replace x with -3: 4 × (-3) + 2.
- = -10
- Answer: -10
f(x) = 5x + 5. Find f(0).
- Replace x with 0: 5 × 0 + 5.
- = 5
- Answer: 5
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
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- Start with Introduction to Function Notation in Context Essentials: Common Mistakes — Reasoning, Introduction to Function Notation in Context Essentials: Common Mistakes — Application, Introduction to Function Notation in Context Essentials: Visual Models. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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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