Domain of Function: Analyzing Fuel Level vs. Distance Traveled

Q: Why can't fuel increase as distance increases?

Cars consume fuel to create energy for movement. Think of it like eating snacks during a movie - the more movie you watch, the fewer snacks you have left!

Q: What does 'always decreasing' mean for this function?

Always decreasing means as one value goes up (distance), the other value goes down (fuel). The fuel tank gets emptier as you drive further.

Q: Could the function ever be increasing?

Only if you add fuel while driving (like refueling). But the basic relationship is consumption, so without refueling, it's always decreasing.

Q: How do I analyze real-world functions like this?

Think about cause and effect:What happens in real life?Does one thing use up or create the other?Apply common sense to mathematical relationships!

Q: What if the car is very fuel-efficient?

Even with excellent fuel efficiency, the car still uses some fuel to travel. Efficiency affects how fast fuel decreases, but it still decreases.

Function Behavior with Real-World Context

Determine which domain corresponds to the function described below:

The function represents the amount of fuel in a car's tank according to the distance traveled by the car.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine which domain corresponds to the function described below:

The function represents the amount of fuel in a car's tank according to the distance traveled by the car.

Step-by-step solution

According to the definition, the amount of fuel in the car's tank will always decrease, since during the trip the car consumes fuel in order to travel.

Therefore, the domain that is suitable for this function is - always decreasing.

Final Answer

Always decreasing

Key Points to Remember

Essential concepts to master this topic

Function Behavior: Real situations determine if values increase or decrease
Fuel Analysis: Distance increases → fuel decreases (consumption)
Verification: Check: more miles driven = less fuel remaining ✓

Common Mistakes

Avoid these frequent errors

Thinking fuel increases with distance
Don't assume fuel increases as you drive = impossible result! Cars consume fuel to move, they don't create it. Always think about the real-world relationship: driving uses fuel, so fuel decreases.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing?

FAQ

Everything you need to know about this question

Why can't fuel increase as distance increases?

Cars consume fuel to create energy for movement. Think of it like eating snacks during a movie - the more movie you watch, the fewer snacks you have left!

What does 'always decreasing' mean for this function?

Always decreasing means as one value goes up (distance), the other value goes down (fuel). The fuel tank gets emptier as you drive further.

Could the function ever be increasing?

Only if you add fuel while driving (like refueling). But the basic relationship is consumption, so without refueling, it's always decreasing.

How do I analyze real-world functions like this?

Think about cause and effect:

What happens in real life?
Does one thing use up or create the other?
Apply common sense to mathematical relationships!

What if the car is very fuel-efficient?

Even with excellent fuel efficiency, the car still uses some fuel to travel. Efficiency affects how fast fuel decreases, but it still decreases.

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