Question
what is the name of the function that matches with this?: Leilany arrived at a red light while driving. What function would represent her distance driven over a period of time?
Answers
GPT-4o mini
The scenario you've described—where Leilany arrives at a red light and likely comes to a stop—can be represented by a piecewise function. This function essentially has different expressions based on the time intervals because her distance driven will change depending on whether she is moving or stopped.
1. While she is driving toward the light and moving, the function can be represented as a linear function of the form \( d(t) = vt \), where \( d \) is distance, \( v \) is her speed, and \( t \) is time.
2. When she comes to a stop at the red light, the distance remains constant for that period of time, so the function could be represented as \( d(t) = d_0 \), where \( d_0 \) is the distance she has traveled at the moment she stops.
Overall, the function might look something like this:
\[
d(t) =
\begin{cases}
vt & \text{for } t < t_0 \\
d_0 & \text{for } t \geq t_0
\end{cases}
\]
This piecewise function captures her movement until she arrives at the red light and then represents her constant distance while stopped.
1. While she is driving toward the light and moving, the function can be represented as a linear function of the form \( d(t) = vt \), where \( d \) is distance, \( v \) is her speed, and \( t \) is time.
2. When she comes to a stop at the red light, the distance remains constant for that period of time, so the function could be represented as \( d(t) = d_0 \), where \( d_0 \) is the distance she has traveled at the moment she stops.
Overall, the function might look something like this:
\[
d(t) =
\begin{cases}
vt & \text{for } t < t_0 \\
d_0 & \text{for } t \geq t_0
\end{cases}
\]
This piecewise function captures her movement until she arrives at the red light and then represents her constant distance while stopped.