Question

In Exercises 15–26, use graphs to find each set. (- 3, 0) ⋃ [- 1, 2]

Accepted Answer

Understand the notation: The symbol $$ \cup $$ represents the union of two sets, meaning all elements that are in either set or both. Identify the sets given: The first set is $$ (-3, 0) $$, which is an open interval including all numbers greater than $$-3$$ and less than $$0$$, but not including $$-3 or$$ $$0. $$The second set is $$ [-1, 2] $$, which is a closed interval including all numbers from $$-1 to$$ $$2$$, including the endpoints $$-1$$ and $$2. $$Visualize the intervals on a number line: Mark the points $$-3$$, $$-1$$, $$0$$, and $$2. $$For $$(-3, 0)$$, draw an open circle at $$-3$$ and $$0$$ and shade the region between them. For $$[-1, 2]$$, draw closed circles at $$-1$$ and $$2$$ and shade the region between them. Determine the union $$ (-3, 0) \cup [-1, 2] $$: Combine all the shaded regions from both intervals. Since $$[-1, 2]$$ overlaps with $$(-3, 0)$$ between $$-1$$ and $$0$$, the union will cover from just greater than $$-3 up to$$ $$2$$, including $$-1$$ and $$2$$ but excluding $$-3$$ and $$0 ($$except where included by the second set). Express the union as an interval or combination of intervals: Based on the combined shading, write the union in interval notation, carefully noting which endpoints are included or excluded.

In Exercises 15–26, use graphs to find each set. (- 3, 0) ⋃ [- 1, 2]

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