Question

select all the intervals where h is increasing.
choose all answers that apply:
a -1.5 < x < -0.5
b 0 < x < 1
c 3.5 < x < 4
d none of the above

Explanation:

Step1: Recall increasing - function property

A function $y = h(x)$ is increasing on an interval if as $x$ increases, $y$ also increases. That is, the slope of the tangent line to the curve is positive on that interval.

Step2: Analyze the given graph

By observing the graph of $y = h(x)$:

• On the interval $-1.5\lt x\lt - 0.5$, the function is decreasing since as $x$ increases from $-1.5$ to $-0.5$, the $y$-values of the function are getting smaller.
• On the interval $0\lt x\lt1$, as $x$ increases from $0$ to $1$, the $y$-values of the function are getting larger. So the function is increasing on the interval $(0,1)$.
• On the interval $3.5\lt x\lt4$, the function is decreasing since as $x$ increases from $3.5$ to $4$, the $y$-values of the function are getting smaller.

Answer:

B. $0 < x < 1$