Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Test a relation against the definition of a function.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
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
Does {(1,4),(2,4),(1,7)} define y as a function of x?
Why this math matters
Check whether a proposed lookup table can return one unambiguous result for each input. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
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.
One input must have one output
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Does {(1,4),(2,4),(1,7)} define y as a function of x?
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 conditions
Input 1 appears with outputs 4 and 7
A repeated input needs a consistent single output.
Develop the calculation
Input 2 appears with output 4
Sharing an output with another input is allowed.
Check and interpret
The relation is not a function of x
The conflicting outputs for input one violate the defining requirement.
The result
The relation is not a function of x
The conflicting outputs for input one violate the defining requirement.
Common mistakes to catch
- Repeated outputs are allowed; conflicting outputs for one input are not.
- A function statement must name which quantity is the 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 {(1,5),(2,5),(3,5)} a function?
Show a hint
Inspect each input separately.
Reveal answer and explanation
Yes
Every input has one output even though all outputs match.
Practice 2
Does the circle x²+y²=1 define all of y as one function of x?
Show a hint
At x=0 there are two y values.
Reveal answer and explanation
No
Both y=1 and y=−1 satisfy the relation; selecting a branch would be an additional restriction.
Take the idea with you
Check whether a proposed lookup table can return one unambiguous result for each input.
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: Find inputs excluded by an expression
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