Free Grade 3 Function Notation in Context Techniques in Examinations: Visual Models — Application Lessons
Free Grade 3 lessons for Function Notation in Context Techniques in Examinations: Visual Models — 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify function notation in context techniques in examinations: visual models — application
Identify function notation in context techniques in examinations: visual models — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain function notation in context techniques in examinations: visual models — application
Explain function notation in context techniques in examinations: visual models — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate function notation in context techniques in examinations: visual models — application
Calculate function notation in context techniques in examinations: visual models — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare function notation in context techniques in examinations: visual models — application
Compare function notation in context techniques in examinations: visual models — 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 Function Notation in Context Techniques in Examinations: Visual Models — 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) = 5x + 8. Find f(3).[1]
- 2.f(x) = 5x − 3. Find f(0).[1]
- 3.f(x) = 3x + 4. Find f(-4).[1]
- 4.f(x) = 2x + 4. Find f(-4).[1]
- 5.f(x) = 3x − 4. Find f(0).[2]
- 6.f(x) = 5x − 3. Find f(4).[2]
- 7.f(x) = 5x − 8. Find f(0).[2]
- 8.f(x) = 4x − 4. Find f(-4).[2]
- 9.f(x) = 6x + 3. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 5x + 7. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 4x + 8. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 2x − 1. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 23
Replace x with 3: 5 × 3 + 8. = 23
2. -3
Replace x with 0: 5 × 0 − 3. = -3
3. -8
Replace x with -4: 3 × (-4) + 4. = -8
4. -4
Replace x with -4: 2 × (-4) + 4. = -4
5. -4
Replace x with 0: 3 × 0 − 4. = -4
6. 17
Replace x with 4: 5 × 4 − 3. = 17
7. -8
Replace x with 0: 5 × 0 − 8. = -8
8. -20
Replace x with -4: 4 × (-4) − 4. = -20
9. f⁻¹(x) = (x − 3) / 6
Write y = 6x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 6.
10. f⁻¹(x) = (x − 7) / 5
Write y = 5x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 5.
11. f⁻¹(x) = (x − 8) / 4
Write y = 4x + 8 and swap x and y. Rearrange for y: y = (x − 8) / 4.
12. f⁻¹(x) = (x + 1) / 2
Write y = 2x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 2.
Worked examples
f(x) = 4x − 1. Find f(-1).
- Replace x with -1: 4 × (-1) − 1.
- = -5
- Answer: -5
f(x) = 5x + 2. Find f(-3).
- Replace x with -3: 5 × (-3) + 2.
- = -13
- Answer: -13
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
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