The function given is \( d = |0.75t - 4| \). This is an absolute value function, which creates a V-shape when graphed.
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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.
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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 \( \frac{16}{3} \).
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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.