Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.