Question

I need help with the graph about it increasing and decreasing!!

Answer 1

Answers:

Increasing:
`(-1.5, 2)`

Decreasing:
`(-\infty,-1.5) \cup (2,\infty)`

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Step-by-step explanation:

A function curve is considered increasing when moving uphill as you move to the right.

We're going uphill on the interval
`-1.5 < \text{x} < 2` which translates to the interval notation
`(-1.5, 2)`. Be sure not to confuse this with ordered pair notation which unfortunately looks identical. The curved parenthesis are used to exclude each endpoint.

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When moving to the right, we go downhill on two separate regions:

• When x < -1.5, aka
  `-\infty < \text{x} < -1.5`
• When x > 2, aka
  `2 < \text{x} < \infty`

The first portion translates to the interval notation
`(-\infty,-1.5)`

The second portion translates to
`(2,\infty)`

We glue those regions together with a union symbol to get
`(-\infty,-1.5) \cup (2,\infty)`

The union symbol basically means "or" when it comes to interval notation. So we are decreasing on the interval
`(-\infty,-1.5)` or decreasing on the interval
`(2,\infty)`