Question

From the graph of the function, determine the domain and the range.

Answer 1

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}

Gathering Both Domain and Range

• 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