Question

determine the open intervals over which the function is increasing, decreasing, or constant. write answers in interval notation. for non - existant intervals enter dne for does not exist.
increasing:
decreasing:
constant:
relative maximum value:
relative maximum point:
relative minimum value:
relative minimum point:
if this a function?
yes, this is a function.
no, this is not a function.
question help: message instructor

Explanation:

Step1: Identify increasing interval

Observe graph rising from $x=-1$ to $x=1$.
Interval: $(-1, 1)$

Step2: Identify decreasing intervals

Observe graph falling from $(-\infty, -1)$ and $(1, \infty)$.
Intervals: $(-\infty, -1)$, $(1, \infty)$

Step3: Check for constant interval

Graph never stays flat; no constant interval.
Result: DNE

Step4: Find relative maximum

Highest peak at $x=1$, $y=3$.
Value: $3$; Point: $(1, 3)$

Step5: Find relative minimum

Lowest valley at $x=-1$, $y=-3$.
Value: $-3$; Point: $(-1, -3)$

Step6: Verify function with vertical line test

No vertical line intersects graph more than once.
Result: Yes, this is a function.

Answer:

Increasing: $(-1, 1)$
Decreasing: $(-\infty, -1)$, $(1, \infty)$
Constant: DNE
Relative Maximum Value: $3$
Relative Maximum Point: $(1, 3)$
Relative Minimum Value: $-3$
Relative Minimum Point: $(-1, -3)$
If this a function? Yes, this is a function.