Free Grade 3 Introduction to Function Notation in Context Essentials: Worked Examples — Mastery Worksheets
Free Grade 3 worksheets for Introduction to Function Notation in Context Essentials: Worked Examples — 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
20 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: worked examples — mastery
Explain introduction to function notation in context essentials: worked examples — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to function notation in context essentials: worked examples — mastery
Calculate introduction to function notation in context essentials: worked examples — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to function notation in context essentials: worked examples — mastery
Compare introduction to function notation in context essentials: worked examples — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to function notation in context essentials: worked examples — mastery
Justify introduction to function notation in context essentials: worked examples — 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: Worked Examples — 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 + 6. Find f(1).[1]
- 2.f(x) = 2x + 8. Find f(-3).[1]
- 3.f(x) = 3x + 5. Find f(6).[1]
- 4.f(x) = 4x + 3. Find f(-2).[1]
- 5.f(x) = 6x + 1. Find f(-3).[2]
- 6.f(x) = 4x − 3. Find f(6).[2]
- 7.f(x) = 2x − 3. Find f(4).[2]
- 8.f(x) = 3x + 3. Find f(-3).[2]
- 9.f(x) = 2x + 4. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 4x + 8. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 3x − 3. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 3x − 4. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 8
Replace x with 1: 2 × 1 + 6. = 8
2. 2
Replace x with -3: 2 × (-3) + 8. = 2
3. 23
Replace x with 6: 3 × 6 + 5. = 23
4. -5
Replace x with -2: 4 × (-2) + 3. = -5
5. -17
Replace x with -3: 6 × (-3) + 1. = -17
6. 21
Replace x with 6: 4 × 6 − 3. = 21
7. 5
Replace x with 4: 2 × 4 − 3. = 5
8. -6
Replace x with -3: 3 × (-3) + 3. = -6
9. f⁻¹(x) = (x − 4) / 2
Write y = 2x + 4 and swap x and y. Rearrange for y: y = (x − 4) / 2.
10. f⁻¹(x) = (x − 8) / 4
Write y = 4x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 4.
11. f⁻¹(x) = (x + 3) / 3
Write y = 3x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 3.
12. f⁻¹(x) = (x + 4) / 3
Write y = 3x − 4 and swap x and y. Rearrange for y: y = (x + 4) / 3.
Worked examples
f(x) = 4x − 7. Find f(0).
- Replace x with 0: 4 × 0 − 7.
- = -7
- Answer: -7
f(x) = 4x + 7. Find f(5).
- Replace x with 5: 4 × 5 + 7.
- = 27
- Answer: 27
f(x) = 2x − 2. Find the inverse f⁻¹(x).
- Write y = 2x − 2 and swap x and y.
- Rearrange for y: y = (x + 2) / 2.
- Answer: f⁻¹(x) = (x + 2) / 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.
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