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.
There is a vertex at open paren 20 comma 0 close paren which indicates that after 20 seconds the train is at the same location as the railroad crossing.

Answer 1

To analyze the function \( d = |600 - 30t| \), let's break down its key features:

1. Understanding the Function:

   • The function represents the distance \( d \) of the train from the railroad crossing as it moves from its starting point of 600 feet away at a speed of 30 feet per second.

2. Finding Key Features:

   • The expression inside the absolute value \( 600 - 30t \) indicates that the distance from the crossing will reach zero when \( 600 - 30t = 0 \). This occurs when \( t = 20 \) seconds.

3. Vertex:

   • At \( t = 20 \), the absolute value function achieves its minimum value of 0, meaning the train reaches the crossing at this time. Thus, the vertex of the function is indeed at the point \( (20, 0) \).

4. Range and Domain:

   • The distance \( d \) cannot be negative, thus the range of the function is \( d \geq 0 \).
   • The time \( t \) can only be non-negative, indicating that the domain is \( t \geq 0 \).

5. Behavior of the Function:

   • The function is not purely increasing or decreasing; it decreases to the vertex and then increases as the train moves away from the crossing after passing it.

Based on the information above, the correct interpretation from the options given would be:

• 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 option correctly identifies the vertex and its significance in the context of the train's motion. The other responses contain incorrect interpretations of the range and domain.