The function d=|0.5t−6|

Question

can be used to determine the distance in floors a person on an elevator is from the 6th floor, where t is the time in seconds since the elevator left the ground floor.

What do the key features of the function reveal?

(1 point)
Responses

The function is a decreasing function and an increasing function, so as the person on the elevator travels from the ground floor to the 6th floor, the distance from the 6th floor decreases at a constant rate and as the person on the elevator travels away from the 6th floor, the distance from 6th floor increases at a constant rate.
The function is a decreasing function and an increasing function, so as the person on the elevator travels from the ground floor to the 6th floor, the distance from the 6th floor decreases at a constant rate and as the person on the elevator travels away from the 6th floor, the distance from 6th floor increases at a constant rate.

The function is an increasing function, so as the person on the elevator travels from the ground floor to the 6th floor, the distance from the 6th floor decreases at a constant rate.
The function is an increasing function, so as the person on the elevator travels from the ground floor to the 6th floor, the distance from the 6th floor decreases at a constant rate.

The function is neither increasing nor decreasing, so as the person on the elevator travels from the ground floor to the 6th floor, the distance from the 6th floor decreases but not at a constant rate and as the person on the elevator travels away from the 6th floor, the distance from 6th floor increases but not at a constant rate.
The function is neither increasing nor decreasing, so as the person on the elevator travels from the ground floor to the 6th floor, the distance from the 6th floor decreases but not at a constant rate and as the person on the elevator travels away from the 6th floor, the distance from 6th floor increases but not at a constant rate.

The function is a decreasing function, so as the person on the elevator travels away from the 6th floor, the distance from 6th floor increases at a constant rate.
The function is a decreasing function, so as the person on the elevator travels away from the 6th floor, the distance from 6th floor increases at a constant rate.

Answer 1

To analyze the function \( d = |0.5t - 6| \), let's break it down.

1. Intercepts and Key Points: The expression inside the absolute value is zero when \( 0.5t - 6 = 0 \), or \( t = 12 \). This is the point in time when the elevator reaches the 6th floor (this calculates the distance from the 6th floor to be zero).

2. Behavior of the Function:

   • For \( t < 12 \): \( 0.5t - 6 < 0 \), thus \( d = 6 - 0.5t \) (the distance decreases as \( t \) approaches 12).
   • For \( t > 12 \): \( 0.5t - 6 > 0 \), thus \( d = 0.5t - 6 \) (the distance increases as \( t \) moves away from 12).

3. Increasing and Decreasing:

   • For \( t < 12 \), the function is decreasing.
   • For \( t > 12 \), the function is increasing.

Based on these observations, the correct interpretation is that both increasing and decreasing behaviors are present:

• As the person on the elevator travels from the ground floor to the 6th floor (i.e., as \( t \) increases from 0 to 12), the distance from the 6th floor decreases at a constant rate (linear decrease).
• After reaching the 6th floor (when \( t > 12 \)), the distance from the 6th floor increases at a constant rate.

Thus, the most accurate response is:

The function is a decreasing function and an increasing function, so as the person on the elevator travels from the ground floor to the 6th floor, the distance from the 6th floor decreases at a constant rate and as the person on the elevator travels away from the 6th floor, the distance from 6th floor increases at a constant rate.