Question

HELP!! What are the intervals for the increasing and decreasing of this graph??

Answer 1

Answer:

Increasing: x < - 4 and x > - 2

decreasing: x ε ( - 4, - 2) OR - 4 < x < - 2

Answer 2

See the attached two images to visually see where the function is increasing and decreasing.  (There's one image for each.)

We identify where a function is increasing based on where the y-values increase as the x-values increase.  In other words, as you move left-to-right, the function is increasing if the function is moving upwards.

We identify where a function is decreasing based on where the y-values decrease as the x-values increase.  In other words, as you move left-to-right, the function is decreasing if the function is moving downwards.

In both cases, while you recognize where it's one or the other based on the y-values, you describe it based on where it's happening, based on the x-values.  The y-values tell you what's happening, the x-values tell you where it's happening.

The function is increasing on the intervals (-infinity, -4) and (-2,infinity).  This is the red highlighted portions.

The function is decreasing on the interval (-4,–2).  This the the blue highlighted portions.