Answer: 1) B [-4, 2) ∪ (2, 5) ∪ (5, ∞)
2) D (-4, -2) ∪ (2, 4)
<u>Step-by-step explanation:</u>
First, you need to understand that "domain" refers to all of the x-values.
Second, you need to understand that an open dot means that the coordinate IS NOT included and a closed dot means that it IS included.
Third, you need to understand interval notation. A bracket [ ] means the value is included - <em>closed dot</em>. A parenthesis ( ) means the value is not included - <em>open dot</em>.
Note 1: If a value has both an open dot and a closed dot, the x-value is included on the graph so is represented with a bracket.
Note 2: infinity is always represented by parenthesis (because you can't actually plot that value).
<u>Graph 1:</u>
The first section of the graph starts at x = -4 with a closed dot (bracket) and has a continuous line to x = -2 with an open dot (parenthesis).
<u>Graph 2:</u>
The next section of the graph starts at x = -2 with a closed dot (bracket) and continues to x = ∞ but has open dots at x = 2 and x = 5.
Notice that x = -2 has a parenthesis in the first section of the graph and a bracket in the next section of the graph. A bracket supersedes parenthesis so x = -2 will have a bracket <em>(refer to Note 1)</em>.
So the graph starts at -4 and ends at infinity but has open dots at 2 and 5. Interval notation will be:
- [-4, 2) <em>-4 is included (closed dot) but 2 is not included (open dot)</em>
- (2, 5)<em> neither 2 nor 5 is included (both are open dots)</em>
- (5, ∞) <em> neither 5 nor ∞ is included (5 is an open dot)</em>
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Part 2 asks when y is negative (below the x-axis).
This occurs when x > 4 (not at x = 4 because y = 0 and is not less than zero)
and between -2 and 4 (not equal to them because y = 0)
