Hey there again! :)
This function is a piecewise function and it's different from previous question.
As you may notice, the graphs are separated and some of coordinate points are not a part of domain and range. That's why we have separate domain and range.
First, let's consider that line graph. The one that contains (-2,0) and (0,-2).
Our domain is the set of all x-values. Only (-2,0) is a closed dot. We use [ ] for closed dot and ( ) for opened dot.
Hence, the first domain is [-2,0)
Next, we find the range of line graph or line segment.
Range is the set of all y-values. Hence, the first range is (-2,0]
We are not done yet! We have to find the second domain and range, which is a curve graph.
From the curve graph, our first point starts from (0,4) and ends at (5,4)
Since (0,4) is an opened dot and (5,4) is a closed dot.
Therefore, the second domain is (0,5]
For the range, the minimum point is (3,2) and maximum point is (0,4) and (5,4). Use the y-coordinate to find range.
Hence, the second range is [2,4}
<u>G</u><u>a</u><u>t</u><u>h</u><u>e</u><u>r</u><u>i</u><u>n</u><u>g</u><u> </u><u>B</u><u>o</u><u>t</u><u>h</u><u> </u><u>D</u><u>o</u><u>m</u><u>a</u><u>i</u><u>n</u><u> </u><u>a</u><u>n</u><u>d</u><u> </u><u>R</u><u>a</u><u>n</u><u>g</u><u>e</u>
- First Domain is [-2,0)
- First Range is (-2,0]
- Second Domain is (0,5]
- Second Range is [2,4]
Combine both domains and ranges.
Hence, the domain is [-2,0] U (0,5] and the range is (-2,0] U [2,4] or The First Choice
Let me know if you have any questions!
Topic: Functions / Domain & Range
