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.

From the given statement ,

is true for g

Given :

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

Lets analyze each option whether it fits into the given domain and range

7 is not in our domain . So g(7) is not possible

x=-13 is in our domain  and 20 is also in our range . So this is true for g.

. This is not true because it is given that g(0)=-2

, -11 does not comes under the range. So this statement is not true.

From the given statement ,

is true for g

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Let's take a look through each of the potential options and see whether they meet our requirements:

A. g(7) = -1

We're told at the beginning of the problem that our domain is restricted to the range [-20, 5]. Our input here, x = 7, is out of that range, which means it's not in the domain and can't be true for the function g.

B. g(-13) = 20

Unlike 7, -13 is in the domain of g since it's between -20 and 5. 20 is also in g's range, since it's between -5 and 45. B could be true for g. We have our answer at this point, but I'll point out why the other two are false, too.

C. g(0) = 2

We know from the question that g(0) = -2, so this is clearly false.

D. g(-4) = -11

-11 is less that -5, which means it lies outside the range of g.

b.my answer is b.

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