Free Grade 3 Introducing Function Notation Common Errors in Examinations: Real-life Applications — Reasoning Flashcards
Free Grade 3 flashcards for Introducing Function Notation Common Errors in Examinations: Real-life Applications — 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.
Free
Higher
25 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: real-life applications — reasoning
Explain introducing function notation common errors in examinations: real-life applications — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing function notation common errors in examinations: real-life applications — reasoning
Calculate introducing function notation common errors in examinations: real-life applications — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing function notation common errors in examinations: real-life applications — reasoning
Compare introducing function notation common errors in examinations: real-life applications — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing function notation common errors in examinations: real-life applications — reasoning
Justify introducing function notation common errors in examinations: real-life applications — 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: Real-life Applications — 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) = 6x + 2. Find f(4).[1]
- 2.f(x) = 6x + 4. Find f(6).[1]
- 3.f(x) = 6x + 2. Find f(-4).[1]
- 4.f(x) = 4x − 6. Find f(1).[1]
- 5.f(x) = 2x + 0. Find f(3).[2]
- 6.f(x) = 6x + 5. Find f(-1).[2]
- 7.f(x) = 6x − 8. Find f(4).[2]
- 8.f(x) = 2x + 8. Find f(0).[2]
- 9.f(x) = 6x + 4. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 3x + 7. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 3x + 0. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 2x + 7. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 26
Replace x with 4: 6 × 4 + 2. = 26
2. 40
Replace x with 6: 6 × 6 + 4. = 40
3. -22
Replace x with -4: 6 × (-4) + 2. = -22
4. -2
Replace x with 1: 4 × 1 − 6. = -2
5. 6
Replace x with 3: 2 × 3 + 0. = 6
6. -1
Replace x with -1: 6 × (-1) + 5. = -1
7. 16
Replace x with 4: 6 × 4 − 8. = 16
8. 8
Replace x with 0: 2 × 0 + 8. = 8
9. f⁻¹(x) = (x − 4) / 6
Write y = 6x + 4 and swap x and y. Rearrange for y: y = (x − 4) / 6.
10. f⁻¹(x) = (x − 7) / 3
Write y = 3x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 3.
11. f⁻¹(x) = (x − 0) / 3
Write y = 3x + 0 and swap x and y. Rearrange for y: y = (x − 0) / 3.
12. f⁻¹(x) = (x − 7) / 2
Write y = 2x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 2.
Worked examples
f(x) = 4x + 2. Find f(0).
- Replace x with 0: 4 × 0 + 2.
- = 2
- Answer: 2
f(x) = 2x + 2. Find f(6).
- Replace x with 6: 2 × 6 + 2.
- = 14
- Answer: 14
f(x) = 4x + 7. Find the inverse f⁻¹(x).
- Write y = 4x + 7 and swap x and y.
- Rearrange for y: y = (x − 7) / 4.
- Answer: f⁻¹(x) = (x − 7) / 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
How mastery is evidenced, and which standards it maps to.
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