Free Grade 3 Working with Function Notation in Context Common Errors: Common Mistakes Flashcards
Free Grade 3 flashcards for Working with Function Notation in Context Common Errors: Common Mistakes: 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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30 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 common errors: common mistakes
Identify working with function notation in context common errors: common mistakes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with function notation in context common errors: common mistakes
Explain working with function notation in context common errors: common mistakes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with function notation in context common errors: common mistakes
Calculate working with function notation in context common errors: common mistakes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with function notation in context common errors: common mistakes
Compare working with function notation in context common errors: common mistakes 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 Common Errors: Common Mistakes 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(-1).[1]
- 2.f(x) = 4x − 2. Find f(3).[1]
- 3.f(x) = 4x + 5. Find f(-2).[1]
- 4.f(x) = 6x + 0. Find f(-1).[1]
- 5.f(x) = 2x − 1. Find f(1).[2]
- 6.f(x) = 5x + 1. Find f(-2).[2]
- 7.f(x) = 5x + 0. Find f(-1).[2]
- 8.f(x) = 5x + 2. Find f(-1).[2]
- 9.f(x) = 6x + 7. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x − 8. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 5x − 8. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 6x + 3. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 0
Replace x with -1: 2 × (-1) + 2. = 0
2. 10
Replace x with 3: 4 × 3 − 2. = 10
3. -3
Replace x with -2: 4 × (-2) + 5. = -3
4. -6
Replace x with -1: 6 × (-1) + 0. = -6
5. 1
Replace x with 1: 2 × 1 − 1. = 1
6. -9
Replace x with -2: 5 × (-2) + 1. = -9
7. -5
Replace x with -1: 5 × (-1) + 0. = -5
8. -3
Replace x with -1: 5 × (-1) + 2. = -3
9. f⁻¹(x) = (x − 7) / 6
Write y = 6x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 6.
10. f⁻¹(x) = (x + 8) / 2
Write y = 2x − 8 and swap x and y. Rearrange for y: y = (x + 8) / 2.
11. f⁻¹(x) = (x + 8) / 5
Write y = 5x − 8 and swap x and y. Rearrange for y: y = (x + 8) / 5.
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) = 3x − 8. Find f(-4).
- Replace x with -4: 3 × (-4) − 8.
- = -20
- Answer: -20
f(x) = 6x + 1. Find f(0).
- Replace x with 0: 6 × 0 + 1.
- = 1
- Answer: 1
f(x) = 2x + 5. Find the inverse f⁻¹(x).
- Write y = 2x + 5 and swap x and y.
- Rearrange for y: y = (x − 5) / 2.
- Answer: f⁻¹(x) = (x − 5) / 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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