Question

What are the domain and range of the function mc008-1.jpg?

mc008-2.jpg
domain: mc008-3.jpg
range: mc008-4.jpg
domain: mc008-5.jpg
range: mc008-6.jpg
domain: mc008-7.jpg
range: mc008-8.jpg
domain: mc008-9.jpg
range: mc008-10.jpg

Answer 1

I can’t see the images you named. Please either upload the graph images or describe each graph (intervals shown, open/closed endpoints, arrows, holes, asymptotes, isolated points). Once I can see or read the graphs I’ll give the exact domain and range for each.

While you get the images, here’s a quick reminder of how to determine domain and range from a graph and common notations to use:

How to find the domain
- Project the graph onto the x-axis: all x-values that have at least one point on the graph.
- If the graph extends left/right without end, include (−∞) or ∞ with parentheses: e.g. (−∞, 3] or (−∞, ∞).
- Closed (filled) endpoints are included: use ] or ]. Open (hollow) dots are excluded: use ) or (.
- Holes: if there is a hole at x = a (no filled point there), exclude a from the domain.
- Vertical asymptotes: exclude the x-value(s) where the asymptote is (e.g. x = 1 gives domain (−∞,1) ∪ (1,∞)).

How to find the range
- Project the graph onto the y-axis: all y-values that appear.
- Use the same rules for endpoints, holes, and horizontal asymptotes (a horizontal asymptote y = b may or may not be included depending on whether the graph actually attains y = b).
- If the graph attains a y-value (there is at least one point with that y), include it; if not (only approached), exclude it.

Examples
- A line segment from x = −2 to x = 3, closed at both ends: domain = [−2, 3].
- Same segment but open at x = 3: domain = [−2, 3).
- A graph with a vertical asymptote at x = 1 (no points at x = 1) otherwise defined for all x: domain = (−∞, 1) ∪ (1, ∞).
- A bowl-shaped parabola opening up with vertex at (0,1): domain = (−∞, ∞), range = [1, ∞).
- A curve that approaches y = 2 but never reaches it: range excludes 2, e.g. (−∞, 2) ∪ (2, ∞) or maybe (2, ∞) depending on other parts of the graph.

If you upload the images or type short descriptions like “solid line from (−2,1) to (3,4) with filled endpoints, plus an open dot at (0,0)” I’ll give domain and range for each mc008-*.