Question

What is the range of the function on the graph?

all real numbers
all real numbers less than or equal to –1
all real numbers less than or equal to 3
all real numbers less than or equal to 0

Answer 1

I don't see the graph — could you upload the image or describe it (especially the highest and lowest y-values shown, and whether any endpoints are open or closed)?

How to determine the range from the graph:
- Look at all y-values that the graph attains. The range is the set of those y-values.
- If the graph extends upward or downward without bound, the range goes to ±∞ accordingly.
- If the graph has a highest or lowest y-value, check whether that point is included (closed dot) or excluded (open dot) to decide ≤ / < or ≥ / >.
- Horizontal asymptotes do not necessarily limit the range unless the curve actually attains that y-value.

Examples using your choices:
- If the graph has a maximum at y = 3 (closed dot) and otherwise goes down without bound, the range is “all real numbers ≤ 3.”
- If it has a maximum at y = 0 (closed) and goes down forever, the range is “all real numbers ≤ 0.”
- If it takes every y-value, choose “all real numbers.”
- If the largest y attained is –1 (closed), choose “all real numbers ≤ –1.”

Send the graph or describe its vertical extent and any closed/open endpoints and I’ll pick the correct option.