Question

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

Explanation:

Step1: Analyze the domain of \( g \)

The domain of \( g \) is \( -1 \leq x \leq 4 \), so \( x \) must be in this interval for \( g(x) \) to be defined.

• For \( g(5) \): \( 5 \) is not in \( [-1, 4] \), so \( g(5) = 12 \) is invalid.

Step2: Analyze the range of \( g \)

The range of \( g \) is \( 0 \leq g(x) \leq 18 \), so \( g(x) \) must be in this interval.

• For \( g(1) \): \( -2 \) is not in \( [0, 18] \), so \( g(1) = -2 \) is invalid.

Step3: Check the given value of \( g(2) \)

We know \( g(2) = 8 \), so \( g(2) = 4 \) is inconsistent with the given information.

Step4: Check \( g(3) \)

\( 3 \) is in the domain \( [-1, 4] \), and \( 18 \) is in the range \( [0, 18] \), so \( g(3) = 18 \) is valid.

Answer:

\( g(3) = 18 \)