Please help me on this math question

Question

Examine the following piecewise function.
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Which statements are true?	Select all that apply.

The function is constant over the interval −2≤x≤2

The function is increasing over the interval −2≤x≤2.

The function is increasing over the interval −8≤x≤−2.

The function is increasing over the interval 2≤x≤3.

The function is decreasing over the interval 3≤x≤7.

Answer 1

That is straight forward. The horizontal axis is X. So you have to select the statement that are true for each interval that is considered in each statement. For example:

The function is constant over the interval −2≤x≤2.

Look at the interval where the horizontal axis goes from -2 to 2. What's happening to the curve? Is it going up, down, is it constant?

Same analysis goes to the other statements

Answer 2

The function is constant over the interval −2≤x≤2 True - there are no breaks or holes.

The function is increasing over the interval −2≤x≤2. False. It's a horizontal line. That's not increasing.

The function is increasing over the interval −8≤x≤−2. True. The line is going up from left to right over that interval.

The function is increasing over the interval 2≤x≤3. False. The line is going down from left to right.

The function is decreasing over the interval 3≤x≤7. True. The line is going down from left to right.

Answer 3

The function is constant over the interval −2≤x≤2

This is true. Looking at the graph, you can see that the slope is 0 (it's a horizontal line) at these points.

The function is increasing over the interval −8≤x≤−2.

This is true. Looking at the graph, the function has a positive slope at these points.

The function is increasing over the interval 2≤x≤3

This is true. Looking at the graph, the function has a steep negative slope at these points.

The function is decreasing over the interval 3≤x≤7.

This is also true. Though the function is less steep than it was at 2≤x≤3, it is still sloping downwards.