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Kenny fills up his snowblower's gas tank as he prepares to clear his driveway. The tank holds $0.5$ gallons of gas, which the owner's manual says should allow for $1.5$ hours of use. The function $F(h)$ represents the amount of fuel, in gallons, remaining in the tank after $h$ hours of use. $\newline$ What is the domain of $F(h)$ ? $\newline$ Choices: $\newline$ (A)all real numbers from $0$ to $0.5$ $\newline$ (B)all whole numbers greater than $1.5$ $\newline$ (C)all real numbers from $0$ to $1.5$ $\newline$ (D)all whole numbers less than $1.5$

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Domain and range of linear functions: word problems

Full solution

Q. Kenny fills up his snowblower's gas tank as he prepares to clear his driveway. The tank holds

0.5

gallons of gas, which the owner's manual says should allow for

1.5

hours of use. The function

F(h)

represents the amount of fuel, in gallons, remaining in the tank after

h

hours of use.

\newline

What is the domain of

F(h)

?

\newline

Choices:

\newline

(A)all real numbers from

0

to

0.5

\newline

(B)all whole numbers greater than

1.5

\newline

(C)all real numbers from

0

to

1.5

\newline

(D)all whole numbers less than

1.5

Understand Function $F(h)$ : Understand the function $F(h)$ and what it represents. $F(h)$ represents the amount of fuel, in gallons, remaining in the tank after $h$ hours of use. We need to determine the range of values that $h$ can take.
Determine Min-Max Values: Determine the minimum and maximum values for $h$ based on the given information. $\newline$ The minimum value for $h$ is $0$ hours, which is when the tank is full before any use. The maximum value for $h$ is $1.5$ hours, which is the duration the snowblower can operate on a full tank according to the owner's manual.
Identify Number Type: Identify the type of numbers $h$ can be. $\newline$ Since $h$ represents time, it can be any real number between the minimum and maximum values, including fractions of an hour. Therefore, $h$ does not have to be a whole number.
Determine Domain of F(h): Determine the domain of F(h) based on the values h can take. $\newline$ The domain of F(h) is all real numbers from $0$ to $1.5$ , as the snowblower can be used for any length of time within this interval until the fuel runs out.

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