Domain & Range: Problem Solving & Reasoning
Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the concepts of Domain and Range within function notation, designed to develop problem-solving and reasoning skills for Grade 8 students.
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Full preview • 12 questions
Domain & Range: Problem Solving & Reasoning
Subject: MathematicsGrade: Grade 8
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Date:
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Given the function f(x) = 3x + 2, find the domain and range when x is any real number.
[3 marks]2.
Determine the domain and range of the function f(x) = √(x - 4).
[3 marks]3.
Identify the domain and range of the linear function f(x) = -2x + 5.
[3 marks]B
Problem Solving & Reasoning
Answer the questions thoughtfully. Show detailed working on the grid.
1.
A function f assigns to each person their age in years. The domain is all ages from 0 to 120. What is the range of this function? Explain your reasoning.
[4 marks]2.
A quadratic function f(x) = -x^2 + 4x + 1 models the height of a ball thrown upwards. Find its domain and range. Justify your answer.
[4 marks]C
Real-world Applications
Apply your understanding to real-world scenarios. Explain your reasoning clearly.
1.
A car rental company charges a flat fee plus a daily rate. The total cost C(x) in dollars for x days is given by C(x) = 50 + 20x. What are the domain and range of this function? Explain.
[4 marks]D
Challenge & Extension
Attempt these challenging problems. Show your detailed reasoning.
1.
Construct a graph of a function with a restricted domain x ≥ 1, where the range is y ≤ 3. Describe the key features of your graph.
[4 marks]2.
Find a function with a domain of all positive real numbers and a range of only positive values. Explain your choice.
[4 marks]E
Mixed Review
Answer the variety of questions below, demonstrating your understanding of domain and range.
1.
Identify the domain and range of the function f(x) = |x - 2|.
[2 marks]2.
Plot the graph of y = 2x + 1 for x in the range [-3, 3]. What is the range?
[3 marks]3.
A piecewise function is defined as f(x) = x for x ≥ 0, and f(x) = -x for x < 0. What are the domain and range?
[3 marks]F
Error Analysis
Identify the mistake in the following problem and correct it.
1.
Student claims that the domain of f(x) = 1/(x - 3) is x ≠ 3. Is this correct? Explain and correct if necessary.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet