Question

Given that a function g has the domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, with g(0) = -2 and g(9) = 6, which of the following statements could be true for g(A)?

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

Answer 1

Statements (A) g(7) = -1 and (D) g(-13) = 20 could be true for the function g(A) because they fit within the provided domain and range, and do not contradict any explicit values given for g(x). Statements (B) and (C) cannot be true due to being outside the range and contradicting a given value, respectively.

Step-by-step explanation:

The question is asking which of the provided statements could be true for a function g given its domain of -20 ≤ x ≤ 5 and range of -5 ≤ g(x) ≤ 45, along with the specific values for g(0) and g(9). Let's evaluate the options:

• (A) g(7) = -1 is within the domain and the range, so it could be true.
• (B) g(-4) = -11 is within the domain, but not within the range because -11 is less than -5, so it cannot be true.
• (C) g(0) = 2 contradicts the given fact that g(0) = -2, so it cannot be true.
• (D) g(-13) = 20 is within the domain and the range, so it could be true.

The statements (A) and (D) could be true for the function g(A) since they are both within the specified domain and range of the function and do not violate any given values of g(x).