Question

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 1

Answer: g(3) = 18

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.

Answer 2

Option 4 is correct.

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.