Question

question 2 of 8
select the correct answer.
given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g.

• g(3) = 18
• g(1) = -2
• g(2) = 4
• g(5) = 12

Explanation:

Step1: Analyze the domain and range

The domain of \( g \) is \( -1 \leq x \leq 4 \), so \( x \) must be between -1 and 4 (inclusive). The range is \( 0 \leq g(x) \leq 18 \), so \( g(x) \) must be between 0 and 18 (inclusive). Also, we know \( g(-1) = 2 \) and \( g(2)=8 \).

Step2: Evaluate each option

• Option 1: \( g(3)=18 \)
• \( x = 3 \) is in the domain (\( -1 \leq 3 \leq 4 \)) and \( 18 \) is in the range (\( 0 \leq 18 \leq 18 \)). This is possible.
• Option 2: \( g(1)= -2 \)
• \( -2 \) is not in the range (\( 0 \leq g(x) \leq 18 \)), so this is false.
• Option 3: \( g(2)=4 \)
• We are given \( g(2) = 8 \), so this is false.
• Option 4: \( g(5)=12 \)
• \( x = 5 \) is not in the domain (\( -1 \leq x \leq 4 \)), so this is false.

Answer:

\( g(3) = 18 \) (the option with this statement)