The function d=|600−30t|

Question

can be used to find the distance a train is from a railroad crossing when starting 600 feet away and traveling 30 feet per second after t seconds.

What do the key features of the function reveal?

(1 point)
Responses

The range is d≤0
, so the distance the train is from the railroad crossing can only be negative values.
The range is d is less than or equal to 0 , so the distance the train is from the railroad crossing can only be negative values.

The domain is t≤0
, so the time the train is traveling can only be negative values.
The domain is t is less than or equal to 0 , so the time the train is traveling can only be negative values.

The function is an increasing function, so as the time increases, the distance the train is from the railroad crossing decreases at a constant rate.
The function is an increasing function, so as the time increases, the distance the train is from the railroad crossing decreases at a constant rate.

There is a vertex at (20,0)
which indicates that after 20 seconds the train is at the same location as the railroad crossing.

Answer 1

Let's analyze the function \( d = |600 - 30t| \) to understand its key features.

1. Understanding the function:

   • The expression \( 600 - 30t \) represents the distance from the train to the crossing. As time \( t \) increases, the train moves closer to the crossing at a rate of 30 feet per second.

2. Breaking down the absolute value:

   • The function will yield two scenarios:
     • When \( 600 - 30t \geq 0 \) (the train is still 600 feet or more from the crossing): \( d = 600 - 30t \)
     • When \( 600 - 30t < 0 \) (the train has passed the crossing): \( d = -(600 - 30t) = 30t - 600 \)

3. Finding the vertex:

   • The condition \( 600 - 30t = 0 \) gives \( t = 20 \) seconds.
   • At this point, the distance \( d = 0 \), meaning the train is at the crossing.

4. Domain and range:

   • The domain of the function, since it is based on time \( t \), is \( t \geq 0 \).
   • The range of the function \( d \) is \( d \geq 0 \) because the distance can't be negative.

5. Behavior of the function:

   • The function is not increasing; it actually decreases from 600 feet to 0 feet as \( t \) goes from 0 to 20 seconds, then increases as time continues past 20 seconds indicating that the train has moved beyond the crossing.

Given the analysis, the correct statement among the responses provided focuses on the vertex:

There is a vertex at (20,0) which indicates that after 20 seconds the train is at the same location as the railroad crossing.

This statement effectively encapsulates a key feature of the function.