Free Grade 3 Introducing Function Notation Essentials in Examinations: Real-life Applications — Mastery Worksheets
Free Grade 3 worksheets for Introducing Function Notation Essentials in Examinations: Real-life Applications — 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing function notation essentials in examinations: real-life applications — mastery
Identify introducing function notation essentials in examinations: real-life applications — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing function notation essentials in examinations: real-life applications — mastery
Explain introducing function notation essentials in examinations: real-life applications — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing function notation essentials in examinations: real-life applications — mastery
Calculate introducing function notation essentials in examinations: real-life applications — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing function notation essentials in examinations: real-life applications — mastery
Compare introducing function notation essentials in examinations: real-life applications — 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 Introducing Function Notation Essentials in Examinations: Real-life Applications — 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 − 6. Find f(6).[1]
- 2.f(x) = 6x + 5. Find f(6).[1]
- 3.f(x) = 6x − 1. Find f(6).[1]
- 4.f(x) = 6x + 2. Find f(5).[1]
- 5.f(x) = 6x + 2. Find f(0).[2]
- 6.f(x) = 3x − 3. Find f(0).[2]
- 7.f(x) = 3x + 3. Find f(5).[2]
- 8.f(x) = 4x + 4. Find f(2).[2]
- 9.f(x) = 4x − 1. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x + 8. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 3x − 2. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 6x + 6. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 12
Replace x with 6: 3 × 6 − 6. = 12
2. 41
Replace x with 6: 6 × 6 + 5. = 41
3. 35
Replace x with 6: 6 × 6 − 1. = 35
4. 32
Replace x with 5: 6 × 5 + 2. = 32
5. 2
Replace x with 0: 6 × 0 + 2. = 2
6. -3
Replace x with 0: 3 × 0 − 3. = -3
7. 18
Replace x with 5: 3 × 5 + 3. = 18
8. 12
Replace x with 2: 4 × 2 + 4. = 12
9. f⁻¹(x) = (x + 1) / 4
Write y = 4x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 4.
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) / 3
Write y = 3x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 3.
12. f⁻¹(x) = (x − 6) / 6
Write y = 6x + 6 and swap x and y. Rearrange for y: y = (x − 6) / 6.
Worked examples
f(x) = 4x + 6. Find f(5).
- Replace x with 5: 4 × 5 + 6.
- = 26
- Answer: 26
f(x) = 5x − 3. Find f(-2).
- Replace x with -2: 5 × (-2) − 3.
- = -13
- Answer: -13
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.
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Frequently asked
- Is this Grade 3 Introducing Function Notation Essentials in Examinations: Real-life Applications — 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 Introducing Function Notation Essentials in Examinations: Real-life Applications — Reasoning, Introducing Function Notation Essentials in Examinations: Real-life Applications — Application, Introducing Function Notation Essentials in Examinations: Common Mistakes. 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 Introducing Function Notation Essentials in Examinations: Real-life Applications — Mastery?
- Move on to What is Introducing Function Notation Essentials in Examinations, Introducing Function Notation Essentials in Examinations: Step-by-step Method, Introducing Function Notation Essentials in Examinations: Worked Examples, Introducing Function Notation Essentials in Examinations: Visual Models, which build directly on this idea.
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