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(7) = -1 B. g(0) = 2 C. g(-4) = -11 D. g(-13) = 20

Answer 1

The correct option is;

D. g(-13) = 20

Explanation:

The given information are;

The domain of the function, g is given as -20 ≤ x ≤ 5

The range of the function, g(x), is given as -5 ≤ g(x) ≤ 45

g(0) =-2 and g(-9) = 6

Therefore, given that the function increases from -2, to 6 as the input variable decreases from 0 to -9

Therefore, if the variable, x, decrease further, to -13, the function will likely increase further, to about 20, while in the variable, x, increases further, to 7, the function may likely decrease to about -1

Therefore, we can get either;

g(-13) = 20 or g(7) = -1

However, the domain of the function is -20 ≤ x ≤ 5, therefore, 7 is outside the domain, giving g(-13) = 20 as the only statement that could be true