which intervals show f(x) increasing? choose two options. -2.5, -1.6 -2, -1 (-1.6, 0 0, 0.8) (0.8, 2)

Explanation:

Step1: Recall increasing - function definition

A function $y = f(x)$ 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 $f(x_1)<f(x_2)$. Graphically, the function is increasing when the graph moves up - ward as we move from left to right.

Step2: Analyze the given graph

Looking at the graph of $y = f(x)$:

• In the interval $[-2.5,-1.6]$, the function is decreasing since the $y$ - values are getting smaller as $x$ increases.
• In the interval $[-2,-1]$, the function is decreasing.
• In the interval $(-1.6,0]$, the function is increasing as the $y$ - values are getting larger as $x$ increases.
• In the interval $[0,0.8)$, the function is increasing as the $y$ - values are getting larger as $x$ increases.
• In the interval $(0.8,2)$, the function is decreasing as the $y$ - values are getting smaller as $x$ increases.

Answer:

$(-1.6,0]$, $[0,0.8)$