Answer:
A) The interval(s) where the function is increasing are: $[-3,-1]$ and $[1,3]$.
B) The interval(s) where the function is decreasing is: $[-1,1]$.
C) The interval(s) where the function is constant is: $[-4,-3]$ and $[3,4]$.
D) The domain of the function is $[-4,4]$.
E) The range of the function is $[-1,3]$.
Explanation:
Sure, here is a step-by-step explanation:
The given graph is a piecewise function consisting of three line segments, so we need to analyze the behavior of the function on each segment.
A) To find the interval(s) where the function is increasing, we look for the parts of the graph where the slope of the line is positive. We see that the function is increasing on the intervals $[-3,-1]$ and $[1,3]$. To write this in interval notation with a union, we can write: $[-3,-1] \cup [1,3]$.
B) To find the interval(s) where the function is decreasing, we look for the parts of the graph where the slope of the line is negative. We see that the function is decreasing on the interval $[-1,1]$. So, the interval where the function is decreasing is $[-1,1]$.
C) To find the interval(s) where the function is constant, we look for the parts of the graph where the slope of the line is zero. We see that the function is constant on the intervals $[-4,-3]$ and $[3,4]$. So, the interval where the function is constant is $[-4,-3] \cup [3,4]$.
D) To find the domain of the function, we need to consider all the values of $x$ for which the function is defined. From the graph, we see that the function is defined for all $x$ in the interval $[-4,4]$. So, the domain of the function is $[-4,4]$.
E) To find the range of the function, we need to consider all the values of $y$ that the function can take. From the graph, we see that the smallest value of $y$ is $-1$ and the largest value is $3$. So, the range of the function is $[-1,3]$.