Let's go through each of the statements to determine which, if any, could be true based on the given information about the function [tex]\( g \)[/tex].
The given information about the function [tex]\( g \)[/tex] includes:
- Domain: [tex]\(-20 \leq x \leq 5\)[/tex]
- Range: [tex]\(-5 \leq g(x) \leq 45\)[/tex]
- [tex]\( g(0) = -2 \)[/tex]
- [tex]\( g(-9) = 6 \)[/tex]
Now, let's analyze each statement one by one:
Statement A: [tex]\( g(0) = 2 \)[/tex]
We are given that [tex]\( g(0) = -2 \)[/tex]. Since this directly contradicts the statement [tex]\( g(0) = 2 \)[/tex], statement A is false.
Statement B: [tex]\( g(7) = -1 \)[/tex]
The domain of the function [tex]\( g \)[/tex] is [tex]\(-20 \leq x \leq 5\)[/tex]. The value [tex]\( x = 7 \)[/tex] is outside of this domain. Since [tex]\( x = 7 \)[/tex] is not within the allowed domain, statement B is false.
Statement C: [tex]\( g(-13) = 20 \)[/tex]
Similarly, the domain of the function [tex]\( g \)[/tex] is [tex]\(-20 \leq x \leq 5\)[/tex]. The value [tex]\( x = -13 \)[/tex] is within this range, so we need to check the range of the function. The range of [tex]\( g \)[/tex] is [tex]\(-5 \leq g(x) \leq 45\)[/tex], and [tex]\( 20 \)[/tex] is within this range. However, without specific information about [tex]\( g(-13) \)[/tex], we can't definitively say this value is correct. But since [tex]\( x = -13 \)[/tex] is within the domain and [tex]\( g(-13) = 20 \)[/tex] would be a valid output within the range, it could potentially be true.
Statement D: [tex]\( g(-4) = -11 \)[/tex]
The range of the function [tex]\( g \)[/tex] is [tex]\(-5 \leq g(x) \leq 45\)[/tex]. The value [tex]\( g(x) = -11 \)[/tex] falls outside this range. Thus, statement D is false.
Conclusion:
None of the statements directly align with the given restrictions and specific values provided for the function [tex]\( g \)[/tex]. Therefore, none of the statements A, B, C, or D could be definitively true based on the given information. From our analysis, it seems that no statement could be true. Thus, the correct interpretation of the answer is:
[tex]\( \boxed{0} \)[/tex]
