Free Grade 3 Working with Function Notation in Context Essentials: Real-life Applications — Reasoning Flashcards
Free Grade 3 flashcards for Working with Function Notation in Context Essentials: 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.
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25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with function notation in context essentials: real-life applications — reasoning
Identify working with function notation in context essentials: real-life applications — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with function notation in context essentials: real-life applications — reasoning
Explain working with function notation in context essentials: real-life applications — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with function notation in context essentials: real-life applications — reasoning
Calculate working with function notation in context essentials: real-life applications — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with function notation in context essentials: real-life applications — reasoning
Compare working with function notation in context essentials: 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 Working with Function Notation in Context Essentials: 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) = 2x + 7. Find f(-2).[1]
- 2.f(x) = 4x − 6. Find f(5).[1]
- 3.f(x) = 5x − 6. Find f(3).[1]
- 4.f(x) = 3x + 8. Find f(-4).[1]
- 5.f(x) = 3x − 1. Find f(2).[2]
- 6.f(x) = 6x − 6. Find f(-4).[2]
- 7.f(x) = 2x + 0. Find f(2).[2]
- 8.f(x) = 2x − 8. Find f(6).[2]
- 9.f(x) = 5x − 3. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 3x − 4. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 3x − 2. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 6x − 3. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 3
Replace x with -2: 2 × (-2) + 7. = 3
2. 14
Replace x with 5: 4 × 5 − 6. = 14
3. 9
Replace x with 3: 5 × 3 − 6. = 9
4. -4
Replace x with -4: 3 × (-4) + 8. = -4
5. 5
Replace x with 2: 3 × 2 − 1. = 5
6. -30
Replace x with -4: 6 × (-4) − 6. = -30
7. 4
Replace x with 2: 2 × 2 + 0. = 4
8. 4
Replace x with 6: 2 × 6 − 8. = 4
9. f⁻¹(x) = (x + 3) / 5
Write y = 5x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 5.
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 + 2) / 3
Write y = 3x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 3.
12. f⁻¹(x) = (x + 3) / 6
Write y = 6x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 6.
Worked examples
f(x) = 5x − 3. Find f(1).
- Replace x with 1: 5 × 1 − 3.
- = 2
- Answer: 2
f(x) = 6x + 5. Find f(2).
- Replace x with 2: 6 × 2 + 5.
- = 17
- Answer: 17
f(x) = 3x + 3. Find the inverse f⁻¹(x).
- Write y = 3x + 3 and swap x and y.
- Rearrange for y: y = (x − 3) / 3.
- Answer: f⁻¹(x) = (x − 3) / 3
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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