Free Grade 3 Rules and Methods in Function Notation in Context Common Errors: Real-life Applications — Application Lessons
Free Grade 3 lessons for Rules and Methods in Function Notation in Context Common Errors: Real-life Applications — Application: 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
Foundation
35 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 common errors: real-life applications — application
Identify rules and methods in function notation in context common errors: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain rules and methods in function notation in context common errors: real-life applications — application
Explain rules and methods in function notation in context common errors: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate rules and methods in function notation in context common errors: real-life applications — application
Calculate rules and methods in function notation in context common errors: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare rules and methods in function notation in context common errors: real-life applications — application
Compare rules and methods in function notation in context common errors: real-life applications — application 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 Common Errors: Real-life Applications — Application 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 + 8. Find f(3).[1]
- 2.f(x) = 3x − 2. Find f(5).[1]
- 3.f(x) = 6x + 3. Find f(-3).[1]
- 4.f(x) = 4x + 1. Find f(2).[1]
- 5.f(x) = 6x + 5. Find f(6).[2]
- 6.f(x) = 3x − 2. Find f(-4).[2]
- 7.f(x) = 2x − 6. Find f(0).[2]
- 8.f(x) = 5x − 8. Find f(0).[2]
- 9.f(x) = 5x − 2. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 4x + 5. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x + 5. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 4x − 2. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 17
Replace x with 3: 3 × 3 + 8. = 17
2. 13
Replace x with 5: 3 × 5 − 2. = 13
3. -15
Replace x with -3: 6 × (-3) + 3. = -15
4. 9
Replace x with 2: 4 × 2 + 1. = 9
5. 41
Replace x with 6: 6 × 6 + 5. = 41
6. -14
Replace x with -4: 3 × (-4) − 2. = -14
7. -6
Replace x with 0: 2 × 0 − 6. = -6
8. -8
Replace x with 0: 5 × 0 − 8. = -8
9. f⁻¹(x) = (x + 2) / 5
Write y = 5x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 5.
10. f⁻¹(x) = (x − 5) / 4
Write y = 4x + 5 and swap x and y. Rearrange for y: y = (x − 5) / 4.
11. f⁻¹(x) = (x − 5) / 6
Write y = 6x + 5 and swap x and y. Rearrange for y: y = (x − 5) / 6.
12. f⁻¹(x) = (x + 2) / 4
Write y = 4x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 4.
Worked examples
f(x) = 6x + 3. Find f(-4).
- Replace x with -4: 6 × (-4) + 3.
- = -21
- Answer: -21
f(x) = 6x + 2. Find f(-2).
- Replace x with -2: 6 × (-2) + 2.
- = -10
- Answer: -10
f(x) = 6x − 6. Find the inverse f⁻¹(x).
- Write y = 6x − 6 and swap x and y.
- Rearrange for y: y = (x + 6) / 6.
- Answer: f⁻¹(x) = (x + 6) / 6
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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