Free Grade 3 Rules and Methods in Introducing Function Notation Word Problems: Real-life Applications — Application Worksheets
Free Grade 3 worksheets for Rules and Methods in 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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15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain rules and methods in introducing function notation word problems: real-life applications — application
Explain rules and methods in introducing function notation word problems: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate rules and methods in introducing function notation word problems: real-life applications — application
Calculate rules and methods in introducing function notation word problems: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare rules and methods in introducing function notation word problems: real-life applications — application
Compare rules and methods in introducing function notation word problems: real-life applications — application accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify rules and methods in introducing function notation word problems: real-life applications — application
Justify rules and methods in 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 Rules and Methods in 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) = 6x + 5. Find f(-2).[1]
- 2.f(x) = 6x − 6. Find f(-1).[1]
- 3.f(x) = 2x − 8. Find f(2).[1]
- 4.f(x) = 4x + 4. Find f(6).[1]
- 5.f(x) = 5x + 2. Find f(-4).[2]
- 6.f(x) = 6x − 3. Find f(0).[2]
- 7.f(x) = 3x − 3. Find f(-2).[2]
- 8.f(x) = 4x − 1. Find f(-4).[2]
- 9.f(x) = 2x + 5. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 2x + 6. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x + 1. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 4x + 6. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -7
Replace x with -2: 6 × (-2) + 5. = -7
2. -12
Replace x with -1: 6 × (-1) − 6. = -12
3. -4
Replace x with 2: 2 × 2 − 8. = -4
4. 28
Replace x with 6: 4 × 6 + 4. = 28
5. -18
Replace x with -4: 5 × (-4) + 2. = -18
6. -3
Replace x with 0: 6 × 0 − 3. = -3
7. -9
Replace x with -2: 3 × (-2) − 3. = -9
8. -17
Replace x with -4: 4 × (-4) − 1. = -17
9. f⁻¹(x) = (x − 5) / 2
Write y = 2x + 5 and swap x and y. Rearrange for y: y = (x − 5) / 2.
10. f⁻¹(x) = (x − 6) / 2
Write y = 2x + 6 and swap x and y. Rearrange for y: y = (x − 6) / 2.
11. f⁻¹(x) = (x − 1) / 6
Write y = 6x + 1 and swap x and y. Rearrange for y: y = (x − 1) / 6.
12. f⁻¹(x) = (x − 6) / 4
Write y = 4x + 6 and swap x and y. Rearrange for y: y = (x − 6) / 4.
Worked examples
f(x) = 2x + 8. Find f(-2).
- Replace x with -2: 2 × (-2) + 8.
- = 4
- Answer: 4
f(x) = 5x − 5. Find f(4).
- Replace x with 4: 5 × 4 − 5.
- = 15
- Answer: 15
f(x) = 5x − 4. Find the inverse f⁻¹(x).
- Write y = 5x − 4 and swap x and y.
- Rearrange for y: y = (x + 4) / 5.
- Answer: f⁻¹(x) = (x + 4) / 5
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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