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Select the correct answer.

Given that a function, [tex]g[/tex], has a domain of [tex]-20 \leq x \leq 5[/tex] and a range of [tex]-5 \leq g(x) \leq 45[/tex], and that [tex]g(0) = -2[/tex] and [tex]g(-9) = 6[/tex], select the statement that could be true for [tex]g[/tex].

A. [tex]g(0) = 2[/tex]
B. [tex]g(7) = -1[/tex]
C. [tex]g(-13) = 20[/tex]
D. [tex]g(-4) = -11[/tex]

Sagot :

GinnyAnswer
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]
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