Free Grade 3 Introducing Function Notation Common Errors in Examinations: Step-by-step Method — Reasoning Lessons
Free Grade 3 lessons for Introducing Function Notation Common Errors in Examinations: Step-by-step Method — 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 common errors in examinations: step-by-step method — reasoning
Explain introducing function notation common errors in examinations: step-by-step method — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing function notation common errors in examinations: step-by-step method — reasoning
Calculate introducing function notation common errors in examinations: step-by-step method — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing function notation common errors in examinations: step-by-step method — reasoning
Compare introducing function notation common errors in examinations: step-by-step method — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing function notation common errors in examinations: step-by-step method — reasoning
Justify introducing function notation common errors in examinations: step-by-step method — 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 Common Errors in Examinations: Step-by-step Method — 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 + 2. Find f(6).[1]
- 2.f(x) = 4x + 5. Find f(2).[1]
- 3.f(x) = 2x + 5. Find f(-2).[1]
- 4.f(x) = 4x − 1. Find f(-1).[1]
- 5.f(x) = 5x − 1. Find f(-2).[2]
- 6.f(x) = 4x − 3. Find f(-4).[2]
- 7.f(x) = 2x + 0. Find f(4).[2]
- 8.f(x) = 5x − 6. Find f(5).[2]
- 9.f(x) = 4x − 5. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 3x − 4. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x + 1. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 5x − 1. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 14
Replace x with 6: 2 × 6 + 2. = 14
2. 13
Replace x with 2: 4 × 2 + 5. = 13
3. 1
Replace x with -2: 2 × (-2) + 5. = 1
4. -5
Replace x with -1: 4 × (-1) − 1. = -5
5. -11
Replace x with -2: 5 × (-2) − 1. = -11
6. -19
Replace x with -4: 4 × (-4) − 3. = -19
7. 8
Replace x with 4: 2 × 4 + 0. = 8
8. 19
Replace x with 5: 5 × 5 − 6. = 19
9. f⁻¹(x) = (x + 5) / 4
Write y = 4x − 5 and swap x and y. Rearrange for y: y = (x + 5) / 4.
10. f⁻¹(x) = (x + 4) / 3
Write y = 3x − 4 and swap x and y. Rearrange for y: y = (x + 4) / 3.
11. f⁻¹(x) = (x − 1) / 6
Write y = 6x + 1 and swap x and y. Rearrange for y: y = (x − 1) / 6.
12. f⁻¹(x) = (x + 1) / 5
Write y = 5x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 5.
Worked examples
f(x) = 3x + 0. Find f(-3).
- Replace x with -3: 3 × (-3) + 0.
- = -9
- Answer: -9
f(x) = 4x − 7. Find f(0).
- Replace x with 0: 4 × 0 − 7.
- = -7
- Answer: -7
f(x) = 4x + 2. Find the inverse f⁻¹(x).
- Write y = 4x + 2 and swap x and y.
- Rearrange for y: y = (x − 2) / 4.
- Answer: f⁻¹(x) = (x − 2) / 4
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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