Question

Select all the intervals where
\[g\] is decreasing.
A coordinate plane. The x-axis scales by one, and the y-axis scales by ten. The graph of y equals g of x is a continuous curve. From left to right, it passes through the point negative five, negative ten and decreases through negative four, negative fifty until it reaches a local minimum at negative two and one-half, negative sixty-five. Then it increases through the point negative one, negative fifty and the y-intercept zero, negative twenty-five. It continues to increases until the local maximum at two and one-half, twelve. Then it decreases through the point four, zero and the point five, negative forty. All values are estimates.
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{\llap{-}1}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{10}\]
\[\small{20}\]
\[\small{\llap{-}10}\]
\[\small{\llap{-}20}\]
\[\small{\llap{-}30}\]
\[\small{\llap{-}40}\]
\[\small{\llap{-}50}\]
\[\small{\llap{-}60}\]
\[\small{\llap{-}70}\]
\[y\]
\[x\]
\[\blueD{y=g(x)}\]
Choose all answers that apply:
A
\[-5<x<-4\]
B
\[-2<x<2\]
C
\[3<x<4\]
D
None of the above

Answer 1

A and C

Reason: g decreases from x = -5 to the local minimum at x = -2.5, so the subinterval -5<x<-4 is decreasing. g also decreases from the local maximum at x = 2.5 to x = 5, so 3<x<4 is decreasing. The interval -2<x<2 lies inside the increasing region, so B is not correct.