Question

Describe the graph of the function.

The domain of the function is
.

The range of the function is
.

The x-intercept of the function is
.

The y-intercept of the function is
.

As x approaches positive infinity, y approaches
.

Answer 1

I don’t see the graph or the function — could you either upload the image of the graph or paste the function equation? With that I can fill in the domain, range, intercepts and the end behavior exactly.

While you get that to me, here’s a quick checklist and how to determine each item from a graph:

- Domain: Look along the x‑axis for all x values that the graph reaches. If it continues left/right with arrows, include ±∞. Pay attention to vertical asymptotes and holes (exclude isolated x where there is a hole).
- Write as interval(s), e.g. (-∞, ∞), (−∞, 2) ∪ (2, ∞), [0,5), etc.

- Range: Look along the y‑axis for all y values the graph attains. Include/exclude endpoints for open/closed circles and consider horizontal asymptotes (they may or may not be part of the range).
- Write as interval(s), e.g. [−1, ∞), (−∞, 3).

- x‑intercept(s): Points where the graph crosses the x‑axis (y = 0). List x-values (or full points), e.g. (2, 0).

- y‑intercept: Value at x = 0 (the point where the graph crosses the y‑axis). If the graph is defined at x = 0, list that point, e.g. (0, 4). If there's a hole at x=0, say “no y‑intercept (hole at x=0).”

- End behavior (as x → +∞ or −∞): Look at the right (or left) end of the graph. If it levels off to a horizontal line, that gives a horizontal asymptote y = L (so y → L). If it increases or decreases without bound, then y → +∞ or y → −∞.

Examples:
- y = 2x + 1: domain = (−∞, ∞), range = (−∞, ∞), x‑intercept = (−1/2, 0), y‑intercept = (0,1), as x → +∞, y → +∞.
- y = 1/(x − 2): domain = (−∞,2) ∪ (2,∞), range = (−∞,0) ∪ (0,∞), no x‑intercept, y‑intercept = (0, −1/2), as x → +∞, y → 0.

Send the graph or equation and I’ll fill in the specific answers.