Free Grade 3 What is Working with Function Notation in Context Techniques — Reasoning Flashcards
Free Grade 3 flashcards for What is Working with Function Notation in Context Techniques — 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify what is working with function notation in context techniques — reasoning
Identify what is working with function notation in context techniques — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain what is working with function notation in context techniques — reasoning
Explain what is working with function notation in context techniques — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate what is working with function notation in context techniques — reasoning
Calculate what is working with function notation in context techniques — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare what is working with function notation in context techniques — reasoning
Compare what is working with function notation in context techniques — 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 What is Working with Function Notation in Context Techniques — 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(6).[1]
- 2.f(x) = 3x − 3. Find f(-1).[1]
- 3.f(x) = 6x − 1. Find f(1).[1]
- 4.f(x) = 2x − 6. Find f(1).[1]
- 5.f(x) = 6x + 2. Find f(-2).[2]
- 6.f(x) = 6x + 4. Find f(-3).[2]
- 7.f(x) = 5x − 2. Find f(0).[2]
- 8.f(x) = 6x + 6. Find f(-3).[2]
- 9.f(x) = 3x + 4. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 6x + 0. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x + 8. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 4x − 6. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 34
Replace x with 6: 6 × 6 − 2. = 34
2. -6
Replace x with -1: 3 × (-1) − 3. = -6
3. 5
Replace x with 1: 6 × 1 − 1. = 5
4. -4
Replace x with 1: 2 × 1 − 6. = -4
5. -10
Replace x with -2: 6 × (-2) + 2. = -10
6. -14
Replace x with -3: 6 × (-3) + 4. = -14
7. -2
Replace x with 0: 5 × 0 − 2. = -2
8. -12
Replace x with -3: 6 × (-3) + 6. = -12
9. f⁻¹(x) = (x − 4) / 3
Write y = 3x + 4 and swap x and y. Rearrange for y: y = (x − 4) / 3.
10. f⁻¹(x) = (x − 0) / 6
Write y = 6x + 0 and swap x and y. Rearrange for y: y = (x − 0) / 6.
11. f⁻¹(x) = (x − 8) / 6
Write y = 6x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 6.
12. f⁻¹(x) = (x + 6) / 4
Write y = 4x − 6 and swap x and y. Rearrange for y: y = (x + 6) / 4.
Worked examples
f(x) = 6x − 8. Find f(6).
- Replace x with 6: 6 × 6 − 8.
- = 28
- Answer: 28
f(x) = 6x + 0. Find f(0).
- Replace x with 0: 6 × 0 + 0.
- = 0
- Answer: 0
f(x) = 3x + 0. Find the inverse f⁻¹(x).
- Write y = 3x + 0 and swap x and y.
- Rearrange for y: y = (x − 0) / 3.
- Answer: f⁻¹(x) = (x − 0) / 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
How mastery is evidenced, and which standards it maps to.
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- Start with What is Working with Function Notation in Context Techniques — Application, What is Working with Function Notation in Context Techniques — Understanding, Rules and Methods in Function Notation in Context Techniques. Each one has its own free lesson, worksheet and quiz.
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- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
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- Move on to What is Working with Function Notation in Context Techniques — Mastery, Working with Function Notation in Context Techniques: Step-by-step Method, Working with Function Notation in Context Techniques: Worked Examples, Working with Function Notation in Context Techniques: Visual Models, which build directly on this idea.
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