Answer:
[tex]-13 <x <-12[/tex] Neither Increasing or Decreasing
[tex]-12 <x <-9[/tex] Increasing
[tex]-9 <x <-6[/tex] Decreasing
[tex]-6 <x <-4[/tex] Increasing
[tex]-4 <x <-1[/tex] Neither Increasing or Decreasing
Step-by-step explanation:
To know if the graph of a function is growing or decreasing you must use the graph to verify what happens when x increases.
If when x increases y decreases, then the function is decreasing.
If when x increases y increases, then the function is growing.
Let's look at the
First interval.
[tex]-13 <x <-12[/tex] Note that the value of y is always equal in this interval, therefore the function is not increasing or decreasing.
Second interval
[tex]-12 <x <-9[/tex]
Note that when x increases from -12 to -10, the value of y increases from y = 1 to y = 3.
Then the function is increasing in this interval
Third interval
[tex]-9 <x <-6[/tex]
Note that when x = -9 y= 8, but when x approaches -6 then y approaches 7.
Therefore in this interval the function is decreasing.
Fourth interval
[tex]-6 <x <-4[/tex]
When x = -6 y = 7 and at the end of the interval when x = -4 then y = 11
The function is increasing.
Fifth interval
[tex]-4 <x <-1[/tex]
The value of y remains constant throughout the interval. So the function is not increasing and it is not decreasing
