Free Grade 3 Introduction to Introducing Function Notation Essentials: Worked Examples — Reasoning Worksheets
Free Grade 3 worksheets for Introduction to Introducing Function Notation Essentials: Worked Examples — Reasoning: 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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35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introduction to introducing function notation essentials: worked examples — reasoning
Explain introduction to introducing function notation essentials: worked examples — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to introducing function notation essentials: worked examples — reasoning
Calculate introduction to introducing function notation essentials: worked examples — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to introducing function notation essentials: worked examples — reasoning
Compare introduction to introducing function notation essentials: worked examples — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to introducing function notation essentials: worked examples — reasoning
Justify introduction to introducing function notation essentials: worked examples — reasoning 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 Introducing Function Notation Essentials: Worked Examples — Reasoning 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) = 4x − 5. Find f(-2).[1]
- 2.f(x) = 5x + 8. Find f(4).[1]
- 3.f(x) = 5x + 2. Find f(6).[1]
- 4.f(x) = 2x + 7. Find f(1).[1]
- 5.f(x) = 2x − 1. Find f(6).[2]
- 6.f(x) = 2x + 7. Find f(0).[2]
- 7.f(x) = 3x − 8. Find f(4).[2]
- 8.f(x) = 2x − 8. Find f(0).[2]
- 9.f(x) = 6x + 2. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 4x − 6. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x + 3. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 2x + 1. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -13
Replace x with -2: 4 × (-2) − 5. = -13
2. 28
Replace x with 4: 5 × 4 + 8. = 28
3. 32
Replace x with 6: 5 × 6 + 2. = 32
4. 9
Replace x with 1: 2 × 1 + 7. = 9
5. 11
Replace x with 6: 2 × 6 − 1. = 11
6. 7
Replace x with 0: 2 × 0 + 7. = 7
7. 4
Replace x with 4: 3 × 4 − 8. = 4
8. -8
Replace x with 0: 2 × 0 − 8. = -8
9. f⁻¹(x) = (x − 2) / 6
Write y = 6x + 2 and swap x and y. Rearrange for y: y = (x − 2) / 6.
10. f⁻¹(x) = (x + 6) / 4
Write y = 4x − 6 and swap x and y. Rearrange for y: y = (x + 6) / 4.
11. f⁻¹(x) = (x − 3) / 6
Write y = 6x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 6.
12. f⁻¹(x) = (x − 1) / 2
Write y = 2x + 1 and swap x and y. Rearrange for y: y = (x − 1) / 2.
Worked examples
f(x) = 2x + 7. Find f(-3).
- Replace x with -3: 2 × (-3) + 7.
- = 1
- Answer: 1
f(x) = 5x − 8. Find f(1).
- Replace x with 1: 5 × 1 − 8.
- = -3
- Answer: -3
f(x) = 6x + 8. Find the inverse f⁻¹(x).
- Write y = 6x + 8 and swap x and y.
- Rearrange for y: y = (x − 8) / 6.
- Answer: f⁻¹(x) = (x − 8) / 6
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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