Answered

-8 -6 -4
-2
81
6
4
2
6
.y
A
2
4
6
∞0
X
For the above graph, state the
interval(s) over which the function
is increasing and the interval(s)
over which is it decreasing.

8 6 4 2 81 6 4 2 6 y A 2 4 6 0 X For the above graph state the intervals over which the function is increasing and the intervals over which is it decreasing class=


Answer :

sqdancefan

Answer:

  • increasing: (-∞, 1) ∪ (3, ∞)
  • decreasing: (1, 3)

Step-by-step explanation:

You want to know the intervals where the graphed function is increasing and decreasing.

Increasing

The function is increasing when the graph goes up to the right. It is increasing to the left of the relative maximum at (1, 5), and again to the right of the relative minimum at (3, 1).

In general, a function increases to a relative maximum, and from a relative minimum.

  intervals of increase: (-∞, 1) and (3, ∞)

Decreasing

The function is decreasing when the graph goes down to the right. It is decreasing to the right of the relative maximum and left of the relative minimum.

  interval of decrease: (1, 3)

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Additional comment

We use round brackets for the end points of the intervals because the function is neither increasing nor decreasing at the point where it changes direction. Those interval end points are not included in the intervals of interest.

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