The Function $f(x$\] Is Given By The Set Of Ordered Pairs $\{(8,-3),(0,4),(1,-5),(2,-1),(-6,10)\}$.Which Is True Regarding The Function?A. $f(-3)=8$B. $f(3)=5$C. $f(8)=0$D. $f(-6)=10$

Introduction

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is often represented as a set of ordered pairs, where each pair consists of an input value and the corresponding output value. In this article, we will explore the function $f(x)$ given by the set of ordered pairs $\{(8,-3),(0,4),(1,-5),(2,-1),(-6,10)\}$ and determine which statement is true regarding the function.

Understanding Ordered Pairs

An ordered pair is a pair of values, usually written in the form $(x, y)$, where $x$ is the input value and $y$ is the output value. In the given set of ordered pairs, each pair represents a point on the graph of the function. For example, the pair $(8,-3)$ represents the point on the graph where the input value is $8$ and the output value is $-3$.

Function Values

A function value is the output value of the function for a given input value. In other words, it is the value of the function at a particular point on the graph. To determine the function value, we need to find the corresponding output value for a given input value. For example, if we want to find the function value of $f(8)$, we need to find the output value corresponding to the input value $8$.

Analyzing the Given Ordered Pairs

Let's analyze the given ordered pairs and determine the function value for each input value.

• For the pair $(8,-3)$, the input value is $8$ and the output value is $-3$. Therefore, $f(8)=-3$.
• For the pair $(0,4)$, the input value is $0$ and the output value is $4$. Therefore, $f(0)=4$.
• For the pair $(1,-5)$, the input value is $1$ and the output value is $-5$. Therefore, $f(1)=-5$.
• For the pair $(2,-1)$, the input value is $2$ and the output value is $-1$. Therefore, $f(2)=-1$.
• For the pair $(-6,10)$, the input value is $-6$ and the output value is $10$. Therefore, $f(-6)=10$.

Evaluating the Statements

Now that we have determined the function value for each input value, let's evaluate the given statements.

• A. $f(-3)=8$: This statement is false because there is no pair in the given set of ordered pairs with an input value of $-3$.
• B. $f(3)=5$: This statement is false because there is no pair in the given set of ordered pairs with an input value of $3$.
• C. $f(8)=0$: This statement is false because we determined earlier that $f(8)=-3$.
• D. $f(-6)=10$: This statement is true because we determined earlier that $f(-6)=10$.

Conclusion

In conclusion, the function $f(x)$ given by the set of ordered pairs $\{(8,-3),(0,4),(1,-5),(2,-1),(-6,10)\}$ is a relation between a set of inputs and a set of possible outputs. We determined the function value for each input value and evaluated the given statements. The only true statement is D. $f(-6)=10$.

Frequently Asked Questions

• Q: What is a function? A: A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range.
• Q: What is an ordered pair? A: An ordered pair is a pair of values, usually written in the form $(x, y)$, where $x$ is the input value and $y$ is the output value.
• Q: How do we determine the function value for a given input value? A: We need to find the corresponding output value for a given input value.

Final Thoughts

In this article, we explored the function $f(x)$ given by the set of ordered pairs $\{(8,-3),(0,4),(1,-5),(2,-1),(-6,10)\}$ and determined which statement is true regarding the function. We analyzed the given ordered pairs, determined the function value for each input value, and evaluated the given statements. The only true statement is D. $f(-6)=10$. We hope this article has provided a clear understanding of the function and its properties.

Introduction

In our previous article, we explored the function $f(x)$ given by the set of ordered pairs $\{(8,-3),(0,4),(1,-5),(2,-1),(-6,10)\}$ and determined which statement is true regarding the function. We analyzed the given ordered pairs, determined the function value for each input value, and evaluated the given statements. In this article, we will provide a Q&A section to further clarify any doubts and provide additional information on the function.

Q&A

Q: What is a function?

A: A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is often represented as a set of ordered pairs, where each pair consists of an input value and the corresponding output value.

Q: What is an ordered pair?

A: An ordered pair is a pair of values, usually written in the form $(x, y)$, where $x$ is the input value and $y$ is the output value. For example, the pair $(8,-3)$ represents the point on the graph where the input value is $8$ and the output value is $-3$.

Q: How do we determine the function value for a given input value?

A: We need to find the corresponding output value for a given input value. To do this, we need to look at the given set of ordered pairs and find the pair that has the same input value as the one we are interested in.

Q: What is the domain of the function?

A: The domain of the function is the set of all possible input values. In this case, the domain is $\{8, 0, 1, 2, -6\}$.

Q: What is the range of the function?

A: The range of the function is the set of all possible output values. In this case, the range is $\{-5, -3, 4, -1, 10\}$.

Q: Can we determine the function value for an input value that is not in the domain?

A: No, we cannot determine the function value for an input value that is not in the domain. The function is only defined for the input values in the domain.

Q: Can we determine the function value for an input value that is in the domain but not in the given set of ordered pairs?

A: No, we cannot determine the function value for an input value that is in the domain but not in the given set of ordered pairs. The function is only defined for the input values in the given set of ordered pairs.

Q: How do we know if a statement about the function is true or false?

A: We can determine if a statement about the function is true or false by looking at the given set of ordered pairs and evaluating the statement based on the information provided.

Q: What is the significance of the function value?

A: The function value represents the output value of the function for a given input value. It is an important concept in mathematics and is used in a wide range of applications, including science, engineering, and economics.

Conclusion

In conclusion, the function $f(x)$ given by the set of ordered pairs $\{(8,-3),(0,4),(1,-5),(2,-1),(-6,10)\}$ is a relation between a set of inputs and a set of possible outputs. We determined the function value for each input value and evaluated the given statements. We also provided a Q&A section to further clarify any doubts and provide additional information on the function. We hope this article has provided a clear understanding of the function and its properties.

Frequently Asked Questions

• Q: What is a function? A: A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range.
• Q: What is an ordered pair? A: An ordered pair is a pair of values, usually written in the form $(x, y)$, where $x$ is the input value and $y$ is the output value.
• Q: How do we determine the function value for a given input value? A: We need to find the corresponding output value for a given input value.

Final Thoughts

In this article, we provided a Q&A section to further clarify any doubts and provide additional information on the function. We hope this article has provided a clear understanding of the function and its properties. If you have any further questions or concerns, please do not hesitate to contact us.