Free Grade 3 Working with Function Notation in Context Essentials: Common Mistakes — Mastery Worksheets
Free Grade 3 worksheets for Working with 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.
Free
Stretch
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with function notation in context essentials: common mistakes — mastery
Explain working with function notation in context essentials: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with function notation in context essentials: common mistakes — mastery
Calculate working with function notation in context essentials: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with function notation in context essentials: common mistakes — mastery
Compare working with function notation in context essentials: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with function notation in context essentials: common mistakes — mastery
Justify working with 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 Working with 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) = 2x − 3. Find f(-2).[1]
- 2.f(x) = 2x − 5. Find f(-3).[1]
- 3.f(x) = 2x − 7. Find f(2).[1]
- 4.f(x) = 4x + 1. Find f(-1).[1]
- 5.f(x) = 4x + 8. Find f(6).[2]
- 6.f(x) = 6x − 1. Find f(0).[2]
- 7.f(x) = 3x + 5. Find f(0).[2]
- 8.f(x) = 5x − 3. Find f(-4).[2]
- 9.f(x) = 3x − 7. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x − 8. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 4x + 2. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 3x − 8. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -7
Replace x with -2: 2 × (-2) − 3. = -7
2. -11
Replace x with -3: 2 × (-3) − 5. = -11
3. -3
Replace x with 2: 2 × 2 − 7. = -3
4. -3
Replace x with -1: 4 × (-1) + 1. = -3
5. 32
Replace x with 6: 4 × 6 + 8. = 32
6. -1
Replace x with 0: 6 × 0 − 1. = -1
7. 5
Replace x with 0: 3 × 0 + 5. = 5
8. -23
Replace x with -4: 5 × (-4) − 3. = -23
9. f⁻¹(x) = (x + 7) / 3
Write y = 3x − 7 and swap x and y. Rearrange for y: y = (x + 7) / 3.
10. f⁻¹(x) = (x + 8) / 2
Write y = 2x − 8 and swap x and y. Rearrange for y: y = (x + 8) / 2.
11. f⁻¹(x) = (x − 2) / 4
Write y = 4x + 2 and swap x and y. Rearrange for y: y = (x − 2) / 4.
12. f⁻¹(x) = (x + 8) / 3
Write y = 3x − 8 and swap x and y. Rearrange for y: y = (x + 8) / 3.
Worked examples
f(x) = 2x + 2. Find f(-2).
- Replace x with -2: 2 × (-2) + 2.
- = -2
- Answer: -2
f(x) = 5x − 8. Find f(6).
- Replace x with 6: 5 × 6 − 8.
- = 22
- Answer: 22
f(x) = 2x + 4. Find the inverse f⁻¹(x).
- Write y = 2x + 4 and swap x and y.
- Rearrange for y: y = (x − 4) / 2.
- Answer: f⁻¹(x) = (x − 4) / 2
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.
Every free resource for Working with Function Notation in Context Essentials: Common Mistakes — Mastery
One concept, one ecosystem — all of it free.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Working with Function Notation in Context Essentials: Common Mistakes — Mastery worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Function Notation in Context Essentials: Common Mistakes — Reasoning, Working with Function Notation in Context Essentials: Common Mistakes — Application, Working with 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.
- What comes next after Working with Function Notation in Context Essentials: Common Mistakes — Mastery?
- Move on to What is Working with Function Notation in Context Essentials, Working with Function Notation in Context Essentials: Step-by-step Method, Working with Function Notation in Context Essentials: Worked Examples, Working with Function Notation in Context Essentials: Visual Models, which build directly on this idea.
Related resources
- Free Working with Function Notation in Context Essentials: Common Mistakes — Mastery quizzes
- Free Working with Function Notation in Context Essentials: Common Mistakes — Mastery flashcards
- Free Working with Function Notation in Context Essentials: Common Mistakes — Mastery lessons
- Free Working with Function Notation in Context Essentials: Common Mistakes — Mastery lesson plans
- Working with Function Notation in Context Essentials: Common Mistakes — Mastery in the knowledge graph
- Free AI Tutor
Stuck on Working with Function Notation in Context Essentials: Common Mistakes — Mastery? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor