The function d=|0.75t−4|

Question

can be used to determine the distance in floors a pulley is from the 4th floor, where t is the time in seconds since the pulley 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 pulley travels away from the 4th floor, the distance from the 4th floor increases at a constant rate.
The function is a decreasing function, so as the pulley travels away from the 4th floor, the distance from the 4th floor increases at a constant rate.

The function is a decreasing function and an increasing function, so as the pulley travels from the ground floor to the 4th floor, the distance from the 4th floor decreases at a constant rate, and as the pulley travels away from the 4th floor, the distance from the 4th floor increases at a constant rate.
The function is a decreasing function and an increasing function, so as the pulley travels from the ground floor to the 4th floor, the distance from the 4th floor decreases at a constant rate, and as the pulley travels away from the 4th floor, the distance from the 4th floor increases at a constant rate.

The function is neither increasing nor decreasing, so as the pulley travels from the ground floor to the 4th floor, the distance from the 4th floor decreases but not at a constant rate and as the pulley travels away from the 4th floor, the distance from the 4th floor increases but not at a constant rate.
The function is neither increasing nor decreasing, so as the pulley travels from the ground floor to the 4th floor, the distance from the 4th floor decreases but not at a constant rate and as the pulley travels away from the 4th floor, the distance from the 4th floor increases but not at a constant rate.

The function is an increasing function, so as the pulley travels from the ground floor to the 4th floor, the distance from the 4th floor decreases at a constant rate.
The function is an increasing function, so as the pulley travels from the ground floor to the 4th floor, the distance from the 4th floor decreases at a constant rate.
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Answer 1

The function given is $d=|0.75t-4|$. This is an absolute value function, which creates a V-shape when graphed.

1. Vertex: The vertex of this function occurs when the expression inside the absolute value is zero, which is when $0.75t-4=0$ or $t=\frac{4}{0.75}=\frac{16}{3}$ seconds.

2. Decreasing and Increasing Intervals:

   • For $t<\frac{16}{3}$, the value inside the absolute value is negative, hence the function is decreasing as $t$ approaches $\frac{16}{3}$ from the left.
   • For $t>\frac{16}{3}$, the value inside is positive, and the function is increasing as $t$ moves away from $\frac{16}{3}$.

3. Distance Interpretation:

   • From $t=0$ seconds (ground floor) to $t=\frac{16}{3}$ seconds (4th floor), the distance from the 4th floor (in floors) decreases.
   • After $t=\frac{16}{3}$ seconds, as the pulley moves away from the 4th floor, the distance increases.

Given these observations, the key features of the function reveal that the correct response is:

The function is a decreasing function and an increasing function, so as the pulley travels from the ground floor to the 4th floor, the distance from the 4th floor decreases at a constant rate, and as the pulley travels away from the 4th floor, the distance from the 4th floor increases at a constant rate.