Question

Use the graph to determine the domain and range of the piecewise defined function.

Domain:

mc001-1.jpg

mc001-2.jpg

mc001-3.jpg

mc001-4.jpg
graph

Answer 1

I can do that, but I can't see the graph images you referenced. Please either attach the graph (or a clear photo of it) or describe it precisely (locations of each piece, whether endpoints are open or closed, and any arrows indicating the graph continues).

While you upload or describe it, here are quick steps you can use to find domain and range yourself, plus how to write the answers:

How to find the domain (x-values):
- Look for the leftmost and rightmost x-values where any part of the graph exists.
- If the graph continues with an arrow left or right, the domain extends to −∞ or +∞ accordingly.
- For each endpoint, note if the dot is filled (include that x) or open (exclude that x).
- Combine contiguous x-intervals with union notation. Example forms:
- Finite closed interval: [a, b]
- Open at one end: (a, b] or [a, b)
- Extends infinitely: (−∞, b], [a, ∞), etc.
- Separate points: {c} or add with unions, e.g. [−2,1) ∪ {2}.

How to find the range (y-values):
- Look for the lowest and highest y-values the graph attains.
- If the graph goes up/down without bound (arrows), include ±∞.
- Again note open vs closed endpoints where the extreme occurs.
- Express in interval/union notation similarly.

If you post the image or describe the exact pieces (for example: "a solid dot at (−3,2), a line from x = −2 to x = 1 with an open dot at x=1, and a ray starting at x=3 going right with arrow"), I’ll compute the exact domain and range and show the interval/union notation.