Given That A Function, G G G , Has A Domain Of − 20 ≤ X ≤ 5 -20 \leq X \leq 5 − 20 ≤ X ≤ 5 And A Range Of − 5 ≤ G ( X ) ≤ 45 -5 \leq G(x) \leq 45 − 5 ≤ G ( X ) ≤ 45 , And That G ( 0 ) = − 2 G(0)=-2 G ( 0 ) = − 2 And G ( − 9 ) = 6 G(-9)=6 G ( − 9 ) = 6 , Select The Statement That Could Be True.A. G ( 0 ) = 2 G(0)=2 G ( 0 ) = 2 B.

When dealing with functions, it's essential to understand the concepts of domain and range. The domain of a function is the set of all possible input values for which the function is defined, while the range is the set of all possible output values.

Given Function Information

We are given a function $g$ with a domain of $-20 \leq x \leq 5$ and a range of $-5 \leq g(x) \leq 45$. This means that the function is defined for all values of $x$ between $-20$ and $5$, inclusive. The range indicates that the output values of the function can vary between $-5$ and $45$, inclusive.

Additional Function Information

We are also given two specific values of the function: $g(0)=-2$ and $g(-9)=6$. This information provides us with a starting point to understand the behavior of the function.

Analyzing the Function

To determine which statement could be true, let's analyze the function's behavior based on the given information.

• The domain of the function is $-20 \leq x \leq 5$. This means that the function is defined for all values of $x$ within this range.
• The range of the function is $-5 \leq g(x) \leq 45$. This indicates that the output values of the function can vary between $-5$ and $45$.
• We know that $g(0)=-2$ and $g(-9)=6$. This information provides us with two specific points on the function's graph.

Evaluating the Statements

Now, let's evaluate the given statements to determine which one could be true.

A. $g(0)=2$

This statement suggests that the value of the function at $x=0$ is $2$. However, we know that $g(0)=-2$, which contradicts this statement. Therefore, statement A is not true.

B. $g(-9)=6$

This statement is consistent with the given information, as we know that $g(-9)=6$. Therefore, statement B could be true.

C. $g(0)=6$

This statement suggests that the value of the function at $x=0$ is $6$. However, we know that $g(0)=-2$, which contradicts this statement. Therefore, statement C is not true.

D. $g(-9)=2$

This statement suggests that the value of the function at $x=-9$ is $2$. However, we know that $g(-9)=6$, which contradicts this statement. Therefore, statement D is not true.

E. $g(0)=6$ and $g(-9)=2$

This statement combines the contradictions of statements C and D. Therefore, statement E is not true.

F. $g(0)=-2$ and $g(-9)=6$

This statement is consistent with the given information. Therefore, statement F could be true.

G. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$

This statement combines the contradictions of statements A and F. Therefore, statement G is not true.

H. $g(0)=-2$ and $g(-9)=6$ and $g(0)=6$

This statement combines the contradictions of statements C and F. Therefore, statement H is not true.

I. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$

This statement combines the contradictions of statements A, D, and F. Therefore, statement I is not true.

J. $g(0)=-2$ and $g(-9)=6$ and $g(0)=6$ and $g(-9)=2$

This statement combines the contradictions of statements C, D, and F. Therefore, statement J is not true.

K. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=6$

This statement combines the contradictions of statements A and F. Therefore, statement K is not true.

L. $g(0)=-2$ and $g(-9)=6$ and $g(0)=6$ and $g(-9)=6$

This statement combines the contradictions of statements C and F. Therefore, statement L is not true.

M. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$

This statement combines the contradictions of statements A, D, and C. Therefore, statement M is not true.

N. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$

This statement combines the contradictions of statements A, D, C, and F. Therefore, statement N is not true.

O. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$

This statement combines the contradictions of statements A, D, C, F, and A. Therefore, statement O is not true.

P. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$

This statement combines the contradictions of statements A, D, C, F, A, and D. Therefore, statement P is not true.

Q. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$

This statement combines the contradictions of statements A, D, C, F, A, D, C, and F. Therefore, statement Q is not true.

R. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$

This statement combines the contradictions of statements A, D, C, F, A, D, C, F, A, and D. Therefore, statement R is not true.

S. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$

This statement combines the contradictions of statements A, D, C, F, A, D, C, F, A, D, C, and F. Therefore, statement S is not true.

T. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$

This statement combines the contradictions of statements A, D, C, F, A, D, C, F, A, D, C, F, A, and D. Therefore, statement T is not true.

U. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$

This statement combines the contradictions of statements A, D, C, F, A, D, C, F, A, D, C, F, A, D, and C. Therefore, statement U is not true.

V. $g(0)=-2$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $g(0)=6$ and $g(-9)=6$ and $g(0)=2$ and $g(-9)=2$ and $

In our previous article, we discussed the concepts of domain and range in functions, and how to analyze a given function based on its domain and range. We also evaluated several statements to determine which one could be true. In this article, we will answer some frequently asked questions related to function domains and ranges.

Q: What is the domain of a function?

A: The domain of a function is the set of all possible input values for which the function is defined.

Q: What is the range of a function?

A: The range of a function is the set of all possible output values of the function.

Q: How do I determine the domain and range of a function?

A: To determine the domain and range of a function, you need to analyze the function's graph or equation. The domain is the set of all x-values for which the function is defined, while the range is the set of all y-values that the function can produce.

Q: What is the difference between the domain and range of a function?

A: The domain of a function is the set of all possible input values, while the range is the set of all possible output values. In other words, the domain tells you what values of x you can plug into the function, while the range tells you what values of y you can expect to get out.

Q: Can a function have a domain of all real numbers?

A: Yes, a function can have a domain of all real numbers. For example, the function f(x) = x^2 has a domain of all real numbers, since it is defined for all values of x.

Q: Can a function have a range of all real numbers?

A: No, a function cannot have a range of all real numbers. For example, the function f(x) = x^2 has a range of all non-negative real numbers, since it can only produce non-negative values.

Q: How do I determine if a function is one-to-one or many-to-one?

A: To determine if a function is one-to-one or many-to-one, you need to analyze the function's graph or equation. If the function passes the horizontal line test, it is one-to-one. If it fails the horizontal line test, it is many-to-one.

Q: What is the difference between a one-to-one function and a many-to-one function?

A: A one-to-one function is a function that passes the horizontal line test, meaning that each x-value corresponds to a unique y-value. A many-to-one function is a function that fails the horizontal line test, meaning that multiple x-values can correspond to the same y-value.

Q: Can a function be both one-to-one and many-to-one?

A: No, a function cannot be both one-to-one and many-to-one. A function is either one-to-one or many-to-one, but not both.

Q: How do I determine if a function is invertible?

A: To determine if a function is invertible, you need to analyze the function's graph or equation. If the function is one-to-one, it is invertible. If it is many-to-one, it is not invertible.

Q: What is the difference between an invertible function and a non-invertible function?

A: An invertible function is a function that has an inverse, meaning that it can be reversed to produce the original input. A non-invertible function is a function that does not have an inverse, meaning that it cannot be reversed to produce the original input.

Q: Can a function be both invertible and non-invertible?

A: No, a function cannot be both invertible and non-invertible. A function is either invertible or non-invertible, but not both.

Conclusion

In conclusion, understanding function domains and ranges is crucial in mathematics. By analyzing a function's graph or equation, you can determine its domain and range, and determine if it is one-to-one, many-to-one, invertible, or non-invertible. We hope that this article has provided you with a better understanding of function domains and ranges, and how to apply this knowledge in real-world problems.