Question

select the correct answer. 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(-4) = -11 d. g(-13) = 20

Explanation:

Step1: Analyze Option A

We know from the problem that \( g(0) = -2 \), so \( g(0)=2 \) is a contradiction. So option A is false.

Step2: Analyze Option B

The domain of the function \( g \) is \( -20\leq x\leq5 \). Since \( 7\) is not in the domain (\( 7>5 \)), \( g(7) \) is not defined. So option B is false.

Step3: Analyze Option C

The range of the function \( g \) is \( -5\leq g(x)\leq45 \). The value \( -11 \) is not in the range (\( -11 < -5 \)), so \( g(-4)=-11 \) is false.

Step4: Analyze Option D

First, check the domain: \( -13 \) is in the domain \( -20\leq -13\leq5 \). Then check the range: \( 20 \) is in the range \( -5\leq20\leq45 \). Also, there is no information contradicting \( g(-13) = 20 \) from the given data (\( g(0)=-2 \) and \( g(-9)=6 \)). So this statement could be true.

Answer:

D. \( g(-13) = 20 \)