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Esteban is filling a 30-gal gas tank at a rate of 10 gal per minute. What is the domain of the function that represents the volume of gas y in the tank after x minutes?

Hint: Remember the domain is the x-values. Imagine them plotted on a coordinate plane where time (minutes) are listed on the x-axis and volume (in gallons) is listed on the y-axis. Find the domain that makes sense in this scenario.

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mhanifa

Answer:

  • 0 ≤ x ≤ 3 or x ∈ [0, 3]

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Filling a tank represents a linear function in its simplest form.

The function would be:

  • y = 10x, where y- volume filled after x minutes

We know that tank level has restrictions, minimum of 0 and maximum of 30 gallons.

It can be shown as:

  • 0 ≤ y ≤ 30

Or, after replacing y with its value in terms of x:

  • 0 ≤ 10x ≤ 30

Which simplifies to:

  • 0 ≤ x ≤ 3

This is the domain of the function.

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