Question

Select all the intervals where
\[h\] is increasing.
A coordinate plane. The x-axis scales by one, and the y-axis scales by zero point five. The graph of y equals h of x is a continuous curve. From left to right, it passes through the point negative four point seven-five, zero and decreases through the point negative four, negative zero point six until the local minimum at negative three, negative one. Then it increases through the point negative two, negative zero point five until the local maximum and x-intercept negative one point five, zero. Then it decreases through the point negative one, negative zero point five and to the local minimum and y-intercept zero, negative one. Then it increases through the point one, negative zero point five and to the local maximum and x-intercept one point five, zero. Then it decreases though the point two, negative zero point five and to the local minimum negative three, negative one. Then it increases through the point four, negative zero point five to the local maximum and x-intercept four point seven-five, zero. All values are estimated.
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{\llap{-}1}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{0.5}\]
\[\small{1}\]
\[\small{1.5}\]
\[\small{2}\]
\[\small{2.5}\]
\[\small{\llap{-}0.5}\]
\[\small{\llap{-}1}\]
\[\small{\llap{-}1.5}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}2.5}\]
\[y\]
\[x\]
\[\blueD{y=h(x)}\]

Answer 1

h is increasing on the open intervals (-3, -1.5), (0, 1.5), and (3, 4.75).

Reason: on each of these intervals the graph rises from a local minimum to the next local maximum.