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Katie is driving from New York City to Boston. When she gets on the highway, she sets her car's cruise control to $60$ miles per hour. She travels at that speed for $2$ hours before exiting the highway. The function $D(t)$ represents the distance Katie has traveled on the highway, $t$ hours after she set her cruise control. $\newline$ What is the domain of $D(t)$ ? $\newline$ Choices: $\newline$ (A) all multiples of $60$ $\newline$ (B) all real numbers from $0$ to $2$ $\newline$ (C) all real numbers from $0$ to $120$ $\newline$ (D) all integers less than or equal to $2$

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Domain and range of linear functions: word problems

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Q. Katie is driving from New York City to Boston. When she gets on the highway, she sets her car's cruise control to

60

miles per hour. She travels at that speed for

2

hours before exiting the highway. The function

D(t)

represents the distance Katie has traveled on the highway,

t

hours after she set her cruise control.

\newline

What is the domain of

D(t)

?

\newline

Choices:

\newline

(A) all multiples of

60

\newline

(B) all real numbers from

0

to

2

\newline

(C) all real numbers from

0

to

120

\newline

(D) all integers less than or equal to

2

Set Cruise Control: Katie sets her cruise control to $60$ miles per hour and travels at that speed for $2$ hours. $\newline$ We need to determine the domain of the function $D(t)$ , which represents the distance traveled over time.
Determine Domain: The domain of a function is the set of all possible input values. Since time, $t$ , is the independent variable, we need to find all possible values of $t$ .
Range of Time: Katie drives for $2$ hours at a constant speed. Therefore, the time $t$ can range from $0$ hours (the moment she starts driving) to $2$ hours (when she exits the highway).
Domain of $D(t)$ : The domain of $D(t)$ is all real numbers from $0$ to $2$ because time can be measured in fractions of hours, not just whole hours or multiples of $60$ .

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