Question

kai is swinging on a trapeze in a circus show. the horizontal distance between kai and the edge of the stage, in meters, is modeled by ( d(t) ) where ( t ) is the time in seconds. the function is graphed below, along with one segment highlighted.

graph of ( d(t) ) vs. ( t ) with a highlighted segment

answer two questions about the highlighted segment.

1. which feature of the graph corresponds to the highlighted segment?

choose 1 answer:
a) midline
b) amplitude
c) period

1. what is the meaning of the highlighted segment?

choose 1 answer:
a) the trapeze is hung 10 meters from the edge of the stage.
b) kai completes a single swing cycle in 10 seconds.
c) the trapeze is 10 meters long.

Explanation:

Question 1

• Midline is a horizontal line through the middle of the graph, not a horizontal segment between peaks.
• Amplitude is the vertical distance from midline to a peak, not horizontal.
• Period is the horizontal length of one full cycle, which matches the highlighted segment between two consecutive peaks (a full cycle's horizontal span).

• Option A: The graph’s y - axis is distance, but the highlighted segment is horizontal (time - related), so it's not about the trapeze’s hanging distance.
• Option B: The period (highlighted segment) represents the time for one full swing cycle. If the horizontal length of the highlighted segment (period) is 10 seconds, it means Kai completes one swing cycle in 10 seconds.
• Option C: The graph is about distance from the stage over time, not trapeze length.

Answer:

C. Period

Question 2