Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
A.
g(0) = 2
B.
g(7) = -1
C.
g(-13) = 20
D.
g(-4) = -11
The correct answer is D.
Since we are given that g(0) = -2, we know that option A (g(0) = 2) is not true.
Since the range of g is -5 ≤ g(x) ≤ 45, option B (g(7) = -1) is not true because -1 is outside the range.
Since the domain of g is -20 ≤ x ≤ 5, option C (g(-13) = 20) is not true because -13 is outside the domain.
However, we are not given any information about g(-4), so it is possible that g(-4) = -11, making option D true.