Question

8
over which interval is the function decreasing?
a ${-4, -1, 2, 3}$
b $(-3, -1), (0.9, 2.6)$
c $(-infty, -4), (2, 3)$
d $(-infty, -3), (-1, 0.9), (2.6, +infty)$

Explanation:

Step1: Define decreasing interval

A function decreases when as $x$ increases, $y$ decreases (graph moves down right).

Step2: Identify decreasing regions

1. From $x=-\infty$ to $x=-3$: graph falls right.
2. From $x=-1$ to $x\approx0.9$: graph falls right.
3. From $x\approx2.6$ to $x=+\infty$: graph falls right.

Step3: Match to options

Compare regions to given choices; matches option D.

Answer:

D. $(-\infty,-3), (-1, 0.9), (2.6, +\infty)$