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Teaching video
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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to decide whether a relation is a function.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Ordered pairs and input-output meaning.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Determine which relation is a function: R = {(1,4),(2,4),(3,7)} or S = {(1,4),(1,6),(3,7)}.
Why this math matters
A function assigns exactly one output to each input; different inputs are allowed to share an output. Define input and output roles before using the word function for a real-world rule.
Set up the model
A useful answer starts with clear assumptions:
- The first coordinate is the input.
- Each relation consists exactly of the listed pairs.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Decide whether a relation is a function
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Determine which relation is a function: R = {(1,4),(2,4),(3,7)} or S = {(1,4),(1,6),(3,7)}.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
R inputs: 1,2,3; outputs: 4,4,7
Each input appears with one output; repeated outputs are permitted.
Apply the relationship
S assigns input 1 to both 4 and 6
One allowed input has two different proposed outputs.
Check and interpret
R is a function; S is not
The uniqueness condition concerns the output for a given input, not the input for a given output.
The result
R is a function; S is not
The uniqueness condition concerns the output for a given input, not the input for a given output.
Common mistakes to catch
- Repeated outputs do not violate the function rule.
- A vertical line meeting a graph at multiple distinct points reveals more than one output for one input.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Is y = x² a function of real x?
Show a hint
Ask how many outputs one fixed input receives.
Reveal answer and explanation
Yes
Every real x has one square, even though opposite inputs can share a square.
Practice 2
Does the full circle x² + y² = 1 define y as a function of x?
Show a hint
Check x = 0.
Reveal answer and explanation
No
At x = 0, both y = 1 and y = −1 satisfy the relation.
Take the idea with you
Define input and output roles before using the word function for a real-world rule.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Read a scatter plot without claiming causation
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