Question

answer 1:
x not quite right - check out the answer explanation.
(0,1)u(3,4)
answer 2:
x thats incorrect - mistakes are part of learning. keep trying!
(0,1)u(3,4)
answer explanation
1
correct answers:
1 (-∞,1)u(3,4)
we can see that there are no constant parts to this graph, the graph decreases, then
then decreases again, then increases again.
the arrow pointing up to the left indicates that this first decrease begins at t = -∞, and you
can see that it turns around at t = 1, so the first interval on which this graph is decreasing is
(-∞,1).
we can see that it begins to decrease again at t = 3 and turns around again at t = 4, so the
second interval on which this graph is decreasing is (3,4).
the function is decreasing on two intervals: (-∞,1) and the interval (3,4). in order to
indicate where the function is decreasing, we unite the two intervals using the union symbol, u
this function is decreasing on (-∞,1)u(3,4).

Explanation:

Step1: Analyze the graph's decreasing intervals

The arrow pointing up to the left means the first decrease starts at \(t = -\infty\) and turns around at \(t = 1\), so the first decreasing interval is \((-\infty,1)\).

Step2: Identify the second decreasing interval

The graph starts to decrease again at \(t = 3\) and turns around at \(t = 4\), so the second decreasing interval is \((3,4)\).

Step3: Combine the intervals

Since the function is decreasing on two intervals \((-\infty,1)\) and \((3,4)\), we use the union symbol \(\cup\) to combine them.

Answer:

\((-\infty,1)\cup(3,4)\)