Question

Use the graph to determine the range.
the arrows on the graph is going in two different directions


Which notations accurately represent the range? Check all that apply.

(–∞, 2) U (2, ∞)
(–∞, –2) U (–2, ∞)
{y|y ∈ R, y ≠ –2}
{y|y ∈ R, y ≠ 2}
y < 2 or y > 2
y < –2 or y > –2

Answer 1

I can’t see the graph from your message. From the answer choices, two different possibilities are present: excluding 2 or excluding −2. Which group is correct depends on the y-value the graph never attains.

Equivalences to help you choose:
- (–∞, 2) ∪ (2, ∞), {y | y ∈ R, y ≠ 2}, and "y < 2 or y > 2" are the same statement (all real y except y = 2).
- (–∞, –2) ∪ (–2, ∞), {y | y ∈ R, y ≠ –2}, and "y < –2 or y > –2" are the same statement (all real y except y = −2).

How to decide from the graph: find the y-value that no point on the graph takes (often shown by a horizontal asymptote or a gap at that y). If that missing y is 2, check the three items that mention 2. If it is −2, check the three items that mention −2.

If you upload the graph or tell me which y-value is missing (2 or −2), I’ll mark the correct choices for you.