select all the intervals where g is increasing.\nchoose all answers that apply:\na -4.5 < x < -4\nb -1 < x <…

Explanation:

Step1: Recall increasing - function property

A function $y = g(x)$ is increasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, we have $g(x_1)<g(x_2)$. Graphically, the function is increasing when the graph is going up as we move from left - to - right.

Step2: Analyze option A

For the interval $-4.5 < x < - 4$, looking at the graph, as $x$ moves from values in the left - hand side of the interval towards the right - hand side, the $y$ - values of the function $y = g(x)$ are going up. So the function is increasing on the interval $-4.5 < x < - 4$.

Step3: Analyze option B

For the interval $-1 < x < 0.5$, as $x$ moves from values in the left - hand side of the interval towards the right - hand side, the $y$ - values of the function $y = g(x)$ are going down. So the function is decreasing on the interval $-1 < x < 0.5$.

Step4: Analyze option C

For the interval $1.5 < x < 2$, as $x$ moves from values in the left - hand side of the interval towards the right - hand side, the $y$ - values of the function $y = g(x)$ are going up. So the function is increasing on the interval $1.5 < x < 2$.

Answer:

A. $-4.5 < x < - 4$, C. $1.5 < x < 2$