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, 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.

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.

Answer 1

To analyze the function \( d = |0.5t - 6| \), we need to look at its behavior as \( t \) changes.

1. Understanding the Absolute Value Function: The expression inside the absolute value, \( 0.5t - 6 \), will cross zero when \( 0.5t = 6 \) or \( t = 12 \). This is the point where the behavior of the function changes.

2. Intervals:

   • For \( t < 12 \): \( 0.5t - 6 < 0 \), thus \( d = -(0.5t - 6) = 6 - 0.5t \). In this interval, \( d \) will decrease as \( t \) increases.
   • For \( t = 12 \): \( d = 0 \).
   • For \( t > 12 \): \( 0.5t - 6 > 0 \), thus \( d = 0.5t - 6 \). In this interval, \( d \) will increase as \( t \) increases.

3. Key Features:

   • As the elevator approaches the 6th floor (from the ground floor), the distance \( d \) decreases at a constant rate until \( t = 12 \) seconds (6th floor).
   • After reaching the 6th floor, as the elevator goes past it, the distance \( d \) increases at a constant rate.

Based on this analysis, the correct 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 the 6th floor increases at a constant rate.