Domain of a Weight Function: Analyzing 3-Year Time Period

Function Behavior with Real-World Contexts

Determine the domain of the following function:

The function represents the weight of a person over a period of 3 years.

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine the domain of the following function:

The function represents the weight of a person over a period of 3 years.

2

Step-by-step solution

Logically, a person's weight is something that fluctuates.

In one week, a person's weight can increase, but in the following week, it can decrease.

Therefore, the domain that suits this function is - partly increasing and partly decreasing.

3

Final Answer

Partly increasing and partly decreasing.

Key Points to Remember

Essential concepts to master this topic
  • Domain Rule: Domain refers to all possible input values (time periods)
  • Technique: Analyze real-world behavior: weight fluctuates up and down over time
  • Check: Verify answer matches realistic expectations for the given scenario ✓

Common Mistakes

Avoid these frequent errors
  • Confusing domain with function behavior
    Don't think domain means how the function increases or decreases = wrong interpretation! Domain is the set of input values (here: 0 to 3 years). Always identify what values the independent variable can take, not how the function behaves.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

What's the difference between domain and function behavior?

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Domain is the set of all possible input values (x-values). Function behavior describes whether the output increases, decreases, or does both. Don't mix them up!

How do I find the domain for a time period?

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For a 3-year period, the domain would be [0, 3] if starting from year 0, or whatever time interval makes sense for the context.

Why does weight fluctuate over time?

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In real life, a person's weight naturally goes up and down due to diet, exercise, health, and daily variations. This makes the function partly increasing and partly decreasing.

Can a function have multiple behaviors?

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Yes! Most real-world functions have different behaviors over different intervals. A weight function might increase during some months and decrease during others.

What if the question asks for domain but shows behavior options?

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Read carefully! Sometimes questions have mismatched titles and answer choices. Focus on what the answer choices are actually asking for, even if the title says something else.

How do I analyze function behavior from a description?

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Think about the real-world context! Weight naturally fluctuates, temperatures rise and fall, and populations grow then decline. Use logical reasoning about the situation.

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