Function Domain Analysis: Energy Level Over Time Intervals

Function Behavior with Real-Life Applications

Determine which domain corresponds to the described function:

The function describes a person's energy level throughout the day.

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Step-by-step written solution

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1

Understand the problem

Determine which domain corresponds to the described function:

The function describes a person's energy level throughout the day.

2

Step-by-step solution

Logically, a person's energy level throughout the day changes and depends on many factors.

On one hand, energy levels rise for example when a person eats or consumes caffeine.

On the other hand, energy levels drop when for example a person moves a lot or exercises.

Therefore, the domain that fits 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 Analysis: Functions can increase, decrease, or do both over time
  • Real-Life Context: Energy levels rise with food/caffeine, drop with exercise
  • Verification: Check if function changes direction at different time intervals ✓

Common Mistakes

Avoid these frequent errors
  • Assuming functions have only one behavior throughout
    Don't think a function must be only increasing or only decreasing = wrong pattern recognition! Real-life functions like energy levels change behavior based on different factors throughout the day. Always consider that functions can have multiple behaviors over their domain.

Practice Quiz

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Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

How can a function be both increasing and decreasing?

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A function can increase in some intervals and decrease in others! For example, your energy might rise after breakfast (increasing) but drop after exercise (decreasing). This creates a function that's partly increasing and partly decreasing.

What does 'domain' mean in this context?

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The domain here refers to the behavior pattern of the function, not the input values. We're analyzing whether the function goes up, down, or both throughout its range.

Why can't energy levels be always increasing?

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Think logically! If energy always increased, you'd have infinite energy by the end of the day. Real life shows energy rises and falls based on activities like eating, sleeping, and exercising.

How do I identify if a real-life function increases or decreases?

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Look for cause-and-effect relationships! Ask: 'What makes this go up?' and 'What makes this go down?' For energy:

  • Up: eating, resting, caffeine
  • Down: exercise, stress, time without food

Is 'impossible to know' ever the right answer?

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Not for well-understood real-life situations! We can predict energy patterns because we understand human biology. Save 'impossible to know' for truly unpredictable or undefined mathematical scenarios.

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