Apologies. I am heavily dyslexic and I find this very difficult to grasp.

I have two graphs with x and r as the variables. I am trying to state the range in which the values of this graph meet a certain criteria.

For graph 1 I have found the range to be +-3 to +-11.1.

And graph 2 has a range of +-2.5 to +-9.8.

Would (-11.1,-3]U[3,11.1) and (-9.8,-2.5]U[2.5,9.8) represent this?

Well, I do not know how you got the range as ± 3 to ± 11.1.

The interpretation of your answer is
-11.1 (excluding) to -3 (including)
together with
3 (including) to 11.1 (excluding).

This means that (-3,3) is excluded from the range. Confirm that this is the case. If the graph shows that (-3,3) is included in the range, then it is simply (-11.1,11.1) (where the two limits are excluded).
It is much easier if we can see the graph.

Please follow the same reasoning for the second problem.

No need to apologize! I'm here to help you understand. Let's go step by step.

To state the range of values that meet a certain criteria for the graphs you mentioned, we can use interval notation. In interval notation, we use square brackets [ ] to represent inclusive endpoints and parentheses ( ) to represent exclusive endpoints.

For graph 1, the range you found is "+-3 to +-11.1". To represent this in interval notation, we write (-11.1, -3] U [3, 11.1).

Let's break down each part of this representation:
- (-11.1, -3]: This interval means all values greater than -11.1 and less than or equal to -3. The parentheses indicate that -11.1 and -3 are not included in the range.
- U: This symbol means "union" and is used to combine intervals.
- [3, 11.1): This interval means all values greater than or equal to 3 and less than 11.1. The square bracket on the left indicates that 3 is included, and the parenthesis on the right indicates that 11.1 is not included in the range.

For graph 2, the range you found is "+-2.5 to +-9.8". To represent this in interval notation, we write (-9.8, -2.5] U [2.5, 9.8).

Similarly, let's break down each part of this representation:
- (-9.8, -2.5]: This interval means all values greater than -9.8 and less than or equal to -2.5.
- U: Indicates the union of intervals.
- [2.5, 9.8): This interval means all values greater than or equal to 2.5 and less than 9.8.

So, in summary, your representations (-11.1,-3]U[3,11.1) and (-9.8,-2.5]U[2.5,9.8) are correct for the given ranges.