Question

give the domain and range of the relation.
a. the domain is $(-infty, infty)$
the range is $(-infty, infty)$
b. the domain is $(-infty, 8)cup(8, infty)$
the range is $(-infty, 0)cup(0, infty)$
c. the domain is $(-infty, 0cup1, infty)$
the range is $(-infty, 8cup9, infty)$
d. the domain is $(-infty, 0)cup(0, infty)$
the range is $(-infty, 8)cup(8, infty)$

Explanation:

Step1: Analyze the graph's domain

The graph has a point at \(x = 0\) (the y - axis intercept), but wait, no—wait, looking at the graph, actually, the graph seems to have a break? Wait, no, the options: Let's recall domain is all x - values, range all y - values. Wait, the correct option: Let's check each option. Option D: Domain is \((-\infty,0)\cup(0,\infty)\) (x can be any except 0), range \((-\infty,8)\cup(8,\infty)\) (y can be any except 8). Wait, but the graph—wait, maybe the graph has a vertical asymptote at x = 0 and horizontal at y = 8? Wait, the blue line: Wait, no, maybe I misread. Wait, the options: Let's check the correct one. Wait, the correct answer is D? Wait, no, wait: Wait, the graph—wait, the line: Wait, maybe the graph has a hole or asymptote. Wait, the options: Option D says domain is all real except 0, range all real except 8. Let's see the graph: the line, when x = 0, is there a point? Wait, the blue line has a point at (0,9)? Wait, no, the y - intercept is at (0,9)? Wait, maybe the graph has a horizontal asymptote at y = 8 and vertical at x = 0. So domain: all x except 0 (\((-\infty,0)\cup(0,\infty)\)), range: all y except 8 (\((-\infty,8)\cup(8,\infty)\)), which is option D.

Answer:

D. The domain is \((-\infty,0)\cup(0,\infty)\)
The range is \((-\infty,8)\cup(8,\infty)\)