Free Grade 3 Introduction to Introducing Function Notation Word Problems: Real-life Applications — Application Lesson Plans
Free Grade 3 lesson plans for Introduction to Introducing Function Notation Word Problems: 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.
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20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introduction to introducing function notation word problems: real-life applications — application
Explain introduction to introducing function notation word problems: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to introducing function notation word problems: real-life applications — application
Calculate introduction to introducing function notation word problems: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to introducing function notation word problems: real-life applications — application
Compare introduction to introducing function notation word problems: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to introducing function notation word problems: real-life applications — application
Justify introduction to introducing function notation word problems: 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 Introduction to Introducing Function Notation Word Problems: 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 − 7. Find f(-3).[1]
- 2.f(x) = 3x + 8. Find f(-3).[1]
- 3.f(x) = 3x + 0. Find f(-3).[1]
- 4.f(x) = 5x + 4. Find f(-2).[1]
- 5.f(x) = 2x − 6. Find f(-4).[2]
- 6.f(x) = 3x − 1. Find f(-3).[2]
- 7.f(x) = 4x − 7. Find f(2).[2]
- 8.f(x) = 5x + 0. Find f(-4).[2]
- 9.f(x) = 3x − 1. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 6x − 4. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x + 7. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 2x + 7. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -16
Replace x with -3: 3 × (-3) − 7. = -16
2. -1
Replace x with -3: 3 × (-3) + 8. = -1
3. -9
Replace x with -3: 3 × (-3) + 0. = -9
4. -6
Replace x with -2: 5 × (-2) + 4. = -6
5. -14
Replace x with -4: 2 × (-4) − 6. = -14
6. -10
Replace x with -3: 3 × (-3) − 1. = -10
7. 1
Replace x with 2: 4 × 2 − 7. = 1
8. -20
Replace x with -4: 5 × (-4) + 0. = -20
9. f⁻¹(x) = (x + 1) / 3
Write y = 3x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 3.
10. f⁻¹(x) = (x + 4) / 6
Write y = 6x − 4 and swap x and y. Rearrange for y: y = (x + 4) / 6.
11. f⁻¹(x) = (x − 7) / 6
Write y = 6x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 6.
12. f⁻¹(x) = (x − 7) / 2
Write y = 2x + 7 and swap x and y. Rearrange for y: y = (x − 7) / 2.
Worked examples
f(x) = 4x + 4. Find f(-4).
- Replace x with -4: 4 × (-4) + 4.
- = -12
- Answer: -12
f(x) = 6x − 1. Find f(3).
- Replace x with 3: 6 × 3 − 1.
- = 17
- Answer: 17
f(x) = 4x − 3. Find the inverse f⁻¹(x).
- Write y = 4x − 3 and swap x and y.
- Rearrange for y: y = (x + 3) / 4.
- Answer: f⁻¹(x) = (x + 3) / 4
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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- Start with Introduction to Introducing Function Notation Word Problems: Real-life Applications — Understanding, Introduction to Introducing Function Notation Word Problems: Real-life Applications — Recognition, Introduction to Introducing Function Notation Word Problems: Common Mistakes. Each one has its own free lesson, worksheet and quiz.
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