Question

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(-4) = -11
B.
g(7) = -1
C.
g(-13) = 20
D.
g(0) = 2

Answer 1

Let's take a look through each of the potential options and see whether they meet our requirements:A. g(7) = -1We're told at the beginning of the problem that our domain is restricted to the range [-20, 5]. Our input here, x = 7, is out of that range, which means it's not in the domain and can't be true for the function g.B. g(-13) = 20Unlike 7, -13 is in the domain of g since it's between -20 and 5. 20 is also in g's range, since it's between -5 and 45. B could be true for g. We have our answer at this point, but I'll point out why the other two are false, too.C. g(0) = 2We know from the question that g(0) = -2, so this is clearly false.D. g(-4) = -11-11 is less that -5, which means it lies outside the range of g.