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(-13) = 20 d. g(-4) = -11

Explanation:

Step1: Analyze Domain and Range

The domain of \( g \) is \( -20 \leq x \leq 5 \), so \( x \) must be in this interval. The range is \( -5 \leq g(x) \leq 45 \), so \( g(x) \) must be in this interval.

Step2: Evaluate Option A

Given \( g(0) = -2 \) (from the problem), so \( g(0) = 2 \) is false.

Step3: Evaluate Option B

\( x = 7 \) is not in the domain \( -20 \leq x \leq 5 \), so \( g(7) \) is undefined. This is false.

Step4: Evaluate Option C

\( x = -13 \) is in the domain (\( -20 \leq -13 \leq 5 \)). \( g(-13) = 20 \), and \( 20 \) is in the range (\( -5 \leq 20 \leq 45 \)). This is possible.

Step5: Evaluate Option D

\( g(-4) = -11 \), but \( -11 \) is not in the range (\( -5 \leq g(x) \leq 45 \), since \( -11 < -5 \)). This is false.

Answer:

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