Free Grade 3 Introduction to Function Notation in Context Techniques: Step-by-step Method — Recognition Worksheets
Free Grade 3 worksheets for Introduction to Function Notation in Context Techniques: Step-by-step Method — 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.
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15 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 techniques: step-by-step method — recognition
Explain introduction to function notation in context techniques: step-by-step method — recognition accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to function notation in context techniques: step-by-step method — recognition
Calculate introduction to function notation in context techniques: step-by-step method — recognition accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to function notation in context techniques: step-by-step method — recognition
Compare introduction to function notation in context techniques: step-by-step method — recognition accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to function notation in context techniques: step-by-step method — recognition
Justify introduction to function notation in context techniques: step-by-step method — 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 Techniques: Step-by-step Method — 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) = 5x + 8. Find f(0).[1]
- 2.f(x) = 3x + 1. Find f(3).[1]
- 3.f(x) = 2x − 1. Find f(-3).[1]
- 4.f(x) = 5x + 8. Find f(5).[1]
- 5.f(x) = 3x − 7. Find f(-2).[2]
- 6.f(x) = 4x − 1. Find f(-3).[2]
- 7.f(x) = 4x − 6. Find f(-2).[2]
- 8.f(x) = 5x + 8. Find f(-4).[2]
- 9.f(x) = 6x − 1. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x + 5. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 2x + 6. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 3x − 6. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 8
Replace x with 0: 5 × 0 + 8. = 8
2. 10
Replace x with 3: 3 × 3 + 1. = 10
3. -7
Replace x with -3: 2 × (-3) − 1. = -7
4. 33
Replace x with 5: 5 × 5 + 8. = 33
5. -13
Replace x with -2: 3 × (-2) − 7. = -13
6. -13
Replace x with -3: 4 × (-3) − 1. = -13
7. -14
Replace x with -2: 4 × (-2) − 6. = -14
8. -12
Replace x with -4: 5 × (-4) + 8. = -12
9. f⁻¹(x) = (x + 1) / 6
Write y = 6x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 6.
10. f⁻¹(x) = (x − 5) / 2
Write y = 2x + 5 and swap x and y. Rearrange for y: y = (x − 5) / 2.
11. f⁻¹(x) = (x − 6) / 2
Write y = 2x + 6 and swap x and y. Rearrange for y: y = (x − 6) / 2.
12. f⁻¹(x) = (x + 6) / 3
Write y = 3x − 6 and swap x and y. Rearrange for y: y = (x + 6) / 3.
Worked examples
f(x) = 2x − 6. Find f(-2).
- Replace x with -2: 2 × (-2) − 6.
- = -10
- Answer: -10
f(x) = 6x − 2. Find f(5).
- Replace x with 5: 6 × 5 − 2.
- = 28
- Answer: 28
f(x) = 5x + 1. Find the inverse f⁻¹(x).
- Write y = 5x + 1 and swap x and y.
- Rearrange for y: y = (x − 1) / 5.
- Answer: f⁻¹(x) = (x − 1) / 5
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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Frequently asked
- Is this Grade 3 Introduction to Function Notation in Context Techniques: Step-by-step Method — Recognition 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 What is Introduction to Function Notation in Context Techniques. 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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- Move on to Introduction to Function Notation in Context Techniques: Step-by-step Method — Understanding, Introduction to Function Notation in Context Techniques: Step-by-step Method — Application, Introduction to Function Notation in Context Techniques: Step-by-step Method — Reasoning, Introduction to Function Notation in Context Techniques: Step-by-step Method — Mastery, which build directly on this idea.
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