Free Grade 3 Introducing Function Notation Techniques in Examinations: Common Mistakes — Reasoning Worksheets
Free Grade 3 worksheets for Introducing Function Notation Techniques in Examinations: Common Mistakes — 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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Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing function notation techniques in examinations: common mistakes — reasoning
Explain introducing function notation techniques in examinations: common mistakes — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing function notation techniques in examinations: common mistakes — reasoning
Calculate introducing function notation techniques in examinations: common mistakes — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing function notation techniques in examinations: common mistakes — reasoning
Compare introducing function notation techniques in examinations: common mistakes — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing function notation techniques in examinations: common mistakes — reasoning
Justify introducing function notation techniques in examinations: common mistakes — 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 Introducing Function Notation Techniques in Examinations: Common Mistakes — 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) = 2x − 5. Find f(-4).[1]
- 2.f(x) = 5x − 5. Find f(-1).[1]
- 3.f(x) = 2x − 6. Find f(6).[1]
- 4.f(x) = 5x − 6. Find f(0).[1]
- 5.f(x) = 3x + 1. Find f(3).[2]
- 6.f(x) = 2x − 2. Find f(4).[2]
- 7.f(x) = 6x + 6. Find f(5).[2]
- 8.f(x) = 3x − 2. Find f(5).[2]
- 9.f(x) = 4x + 1. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 5x + 8. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x − 2. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 6x + 0. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -13
Replace x with -4: 2 × (-4) − 5. = -13
2. -10
Replace x with -1: 5 × (-1) − 5. = -10
3. 6
Replace x with 6: 2 × 6 − 6. = 6
4. -6
Replace x with 0: 5 × 0 − 6. = -6
5. 10
Replace x with 3: 3 × 3 + 1. = 10
6. 6
Replace x with 4: 2 × 4 − 2. = 6
7. 36
Replace x with 5: 6 × 5 + 6. = 36
8. 13
Replace x with 5: 3 × 5 − 2. = 13
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) / 5
Write y = 5x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 5.
11. f⁻¹(x) = (x + 2) / 6
Write y = 6x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 6.
12. f⁻¹(x) = (x − 0) / 6
Write y = 6x + 0 and swap x and y. Rearrange for y: y = (x − 0) / 6.
Worked examples
f(x) = 4x − 2. Find f(4).
- Replace x with 4: 4 × 4 − 2.
- = 14
- Answer: 14
f(x) = 5x − 1. Find f(6).
- Replace x with 6: 5 × 6 − 1.
- = 29
- Answer: 29
f(x) = 6x + 6. Find the inverse f⁻¹(x).
- Write y = 6x + 6 and swap x and y.
- Rearrange for y: y = (x − 6) / 6.
- Answer: f⁻¹(x) = (x − 6) / 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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- Start with Introducing Function Notation Techniques in Examinations: Common Mistakes — Application, Introducing Function Notation Techniques in Examinations: Common Mistakes — Understanding, Introducing Function Notation Techniques in Examinations: Visual Models. Each one has its own free lesson, worksheet and quiz.
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