Question

Given that a function, g, has a domain of -20 less than or equal to x less than or equal to 5 and a range of -5 less than or equal to g(x) less than or equal to 45 and that g (0) = -2 and g(-9) = 6, select the statement that could be true for g.A. g(7) = -1B. g(0) = 2C. g(-13) = 20D. g(-4) = -11Please help ASAP​

Answer 1

The function g has a domain and range defined, and we need to determine which statement about the function could be true.

Step-by-step explanation:

The given function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45. To determine which statement could be true for g, we need to check if the given values for g(0) and g(-9) are consistent with the function's domain and range.

Since g(0) = -2 is within the range of -5 ≤ g(x) ≤ 45 and g(-9) = 6 is also within the range, we can conclude that g is a valid function. Now let's check the options:

A. g(7) = -1: This statement is not consistent with the given range, so it is not true.

B. g(0) = 2: This statement is not consistent with the given g(0) value, so it is not true.

C. g(-13) = 20: This statement is not within the domain of -20 ≤ x ≤ 5, so it is not true.

D. g(-4) = -11: This statement is consistent with the given range and g(-4) falls within the domain, so it is true.

Therefore, the statement that could be true for g is D. g(-4) = -11.