Answer:
R: -9 < y < ∞
(option D)
Explanation:
So, the range of a function/relation is all possible y-values
(the domain is all possible x-values)
So, from looking at this graph, we can see where there is a y-value.
We can first ask ourselves: what is the highest possible y-value of this function?
Because there is an arrow approaching infinity, we can assume that the greatest possible y-value is ∞.
(note: our y < ∞ ; not ≤ ∞. This is because even though the y-value is approaching infinity, it can never truly be equal to infinity)
Next, we can observe: what is the lowest possible y-value of this function?
We can see that there is an asymptote {a curve constantly approaching, yet never reaching a value} at -9. This means that our y-value will never reach -9, so every possible y-value must be [at least slightly] greater than -9.
(note: our y > -9, not ≥ -9, because it is not possible for the y-value to truly be equal to -9)
So, if we combine this information:
y > -9
y < ∞
-9 < y < ∞
(We put R: in front of our range to signify that it is range--as opposed to domain)
Hope this helps!!