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 (1) = - 2

g (2) = 4

g (3) = 18

Answer: g (3) = 18

Step-by-step explanation:

The inputs and outputs of the function need to be within the domain and range of the function.

The statement g (5) = 12 cannot be true, because the input, 5, is not in the domain of the function.

The statement g (1) = - 2 cannot be true, because the output, - 2, is not in the range of the function.

For a relation to be a function, each input, x, in the domain can have exactly one output, g (x), in the range. It is given that g (x) is a function.

Option 4 is correct.

Step-by-step explanation:

Consider a function g, it has a domain of - 1 ≤ x ≤ 4 and a range of 0 ≤ g (x) ≤ 18. It is given that g (-1) = 2 and g (2) = 8.

The statement g (5) = 12 is not true because the value of x is 5 which is not in its domain.

The statement g (1) = - 2 is not true because the value of function g (x) is - 2 which is not in its range.

The statement g (2) = 4 is not true because g is a function and each function has unique output for each input value.

If g (2) = 8 and g (2) = 4, then the value of g (x) is 8 and 4 at x=2. It means g (x) is not a function, which is contradiction of given statement.

The statement g (3) = 18 is true because the value of x is 3 which is in the domain and the value of function g (x) is 18 which is in its range.

Therefore, the correct option is 4.