Question

Please help with these graph problems - thank you in advance! There are two!

Answer 1

Answer:  1) B  [-4, 2) ∪ (2, 5) ∪ (5, ∞)

               2) D (-4, -2) ∪ (2, 4)

Step-by-step explanation:

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 - closed dot.  A parenthesis ( ) means the value is not included - open dot.  

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).

Graph 1:

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).

Graph 2:

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 (refer to Note 1).

So the graph starts at -4 and ends at infinity but has open dots at 2 and 5.  Interval notation will be:

• [-4, 2)   -4 is included (closed dot) but 2 is not included (open dot)
• (2, 5)     neither 2 nor 5 is included (both are open dots)
• (5, ∞)    neither 5 nor ∞ is included (5 is an open dot)

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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)

• (-4, -2)
• (2, 4)