Free Grade 3 Rules and Methods in Function Notation in Context Essentials: Visual Models — Understanding Flashcards
Free Grade 3 flashcards for Rules and Methods in Function Notation in Context Essentials: Visual Models — Understanding: 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 rules and methods in function notation in context essentials: visual models — understanding
Identify rules and methods in function notation in context essentials: visual models — understanding accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain rules and methods in function notation in context essentials: visual models — understanding
Explain rules and methods in function notation in context essentials: visual models — understanding accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate rules and methods in function notation in context essentials: visual models — understanding
Calculate rules and methods in function notation in context essentials: visual models — understanding accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare rules and methods in function notation in context essentials: visual models — understanding
Compare rules and methods in function notation in context essentials: visual models — understanding 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 Rules and Methods in Function Notation in Context Essentials: Visual Models — Understanding 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) = 3x − 4. Find f(-3).[1]
- 2.f(x) = 3x + 2. Find f(0).[1]
- 3.f(x) = 5x − 2. Find f(2).[1]
- 4.f(x) = 5x − 6. Find f(0).[1]
- 5.f(x) = 4x + 7. Find f(6).[2]
- 6.f(x) = 4x + 3. Find f(2).[2]
- 7.f(x) = 2x + 7. Find f(-3).[2]
- 8.f(x) = 2x + 0. Find f(2).[2]
- 9.f(x) = 3x + 6. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 3x + 1. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 3x − 4. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 4x + 3. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -13
Replace x with -3: 3 × (-3) − 4. = -13
2. 2
Replace x with 0: 3 × 0 + 2. = 2
3. 8
Replace x with 2: 5 × 2 − 2. = 8
4. -6
Replace x with 0: 5 × 0 − 6. = -6
5. 31
Replace x with 6: 4 × 6 + 7. = 31
6. 11
Replace x with 2: 4 × 2 + 3. = 11
7. 1
Replace x with -3: 2 × (-3) + 7. = 1
8. 4
Replace x with 2: 2 × 2 + 0. = 4
9. f⁻¹(x) = (x − 6) / 3
Write y = 3x + 6 and swap x and y. Rearrange for y: y = (x − 6) / 3.
10. f⁻¹(x) = (x − 1) / 3
Write y = 3x + 1 and swap x and y. Rearrange for y: y = (x − 1) / 3.
11. f⁻¹(x) = (x + 4) / 3
Write y = 3x − 4 and swap x and y. Rearrange for y: y = (x + 4) / 3.
12. f⁻¹(x) = (x − 3) / 4
Write y = 4x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 4.
Worked examples
f(x) = 6x − 1. Find f(-2).
- Replace x with -2: 6 × (-2) − 1.
- = -13
- Answer: -13
f(x) = 4x + 3. Find f(-4).
- Replace x with -4: 4 × (-4) + 3.
- = -13
- Answer: -13
f(x) = 2x − 8. Find the inverse f⁻¹(x).
- Write y = 2x − 8 and swap x and y.
- Rearrange for y: y = (x + 8) / 2.
- Answer: f⁻¹(x) = (x + 8) / 2
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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